Addendum to address the misunderstandings that have become apparent in the comments:
What is being discussed here, is not to encourage women to play chess against their will or to fulfill some other agenda. It's about the fact that there exists an active discouraging attitude towards women in the chess world. Namely, the disrespectful attitude that players have become accustomed to, the dismissal of female players in media coverage and in the literature, the cultural bias against women playing chess (even in the west mind you) where either from childhood girls are told chess is not for them, and similarly in society.
Examples will help: (I'll avoid giving names and titles, the intent here is not to disparage people/clubs/books etc, but to give the reader an idea of the explicit discouragement that exists)
Go to any local club, almost irrespective of where you live, what you will typically witness is:
Players acting in dismay when resigning against a female player, commonly not agreeing to stay for post-mortem analysis (neither of which they have a problem with against male players), their fellow colleagues laughing at their friend for losing to a woman. This attitude is witnessed and passed on to the younger generation: boys constantly mock one another saying "haha you lost to a girl", which means this idea has already been seeded in their heads that boys are supposed to be smarter than girls. Coaches and trainers making comments to (boys) team about them being able to beat anyone in the women's team. Team coaches favoring to select men players to complete their team despite there being stronger female players in the club. Your typical first encounter with your teammates is "oh so you're the exception to the rule, it's nice to see women play chess..."
In the media coverage and literature, often there's a clear disregard towards women, e.g. books starting off in their preface by saying "they will refer to a hypothetical chess player as a he for as long as there hasn't been a female world champion!" In other words, they're saying "I'll start respecting women in chess when they become one day world champion." Or worse, books trying to give analogies for a chess concept and including sexist remarks such as: "For the lady chess player, I would use the comparison with buying clothes corresponding to latest fashion...". And sadly, the list goes on and on... A lot of these things are not just inherent to the chess world.
So as things stand, the scene is not at an equal footing for men and women, instead, female chess players are being constantly disheartened from playing the game they love, or being discouraged from pursuing it. So the discussions here are not about preferential treatment, it's about fighting against the clear bias that exists and how to give boys and girls equal chance and same level of enthusiasm to find out about this beautiful game.
Luckily, not all is lost, nowadays there are many players both men and women who are actively fighting and making a difference in this matter.
End of addendum.
Your first suggestion of separated events already sets the wrong agenda, and here I'll try to focus mostly on this aspect. Not only does the separation create the false assumption in young players' minds that the two genders cannot play at the same level, but it also lowers the number of competitions and the diversity in opponents.This would be a major setback, considering that as is there are currently far less girls getting into chess due to wrongly seeded cultural biases. I strongly recommend reading Judit Polgar's article on the importance of mixed competitions. However, as pointed out in the comments by user Greg Martin (see addendum 3), one shouldn't be completely dismissive towards female-only events either, as they do provide an inclusive safe-space to start competing in.
So first suggestions I'd have are:
Level the playing field: Organize mixed events! There should be no separation between men and women in chess, which is a purely intellectual endeavor, just like fields of mathematics or biology are.
Create a healthy environment: Prevent wrong biases from being perpetuated, as a coach or parent. Don't call a girl being good at chess as being the exception. Be encouraging towards children, and have same level of considerations towards boy and girls playing the game. If you teach or analyse games for a group of people, don't be dismissive towards the games played by your female students, and provide studies and coverage of high level chess from a diversified set of players, irrespective of their gender. This increase the chances of each of your students in finding both a playing style closer to their own and also a character that resonates with them.
To be encouraging and to popularize the game, it is absolutely mandatory to stand up against assumptions against gender bias which can makes themselves apparent in how we talk about chess players (e.g. not assuming a hypothetical chess player is male, see these discussions (1), (2) on the matter), how we write about the game (many famous chess books start outright making sexist remarks in their preface towards a potential female reader), and in our ways and manners when playing the game (related, here).
Instead of being encouraging towards women, often even the high ranking renown players feel entitled to make the utmost ungrounded misogynistic comments about women in the game. I quote below from an article on the Guardian, titled "The World Chess Championship is thrilling. But where are the women?":
More concerning is the realisation that these unproven arguments are
not confined to the niche world of online chess communities.
High-ranking male chess players have a long history of making
disparaging and misogynistic remarks about women and chess. Bobby
Fischer, in what would turn out be one of his tamer offensive
opinions, suggested in a 1963 interview that women were terrible chess
players because “they’re not so smart”. Half a century later the men
are still at it, with British grandmaster Nigel Short arguing in 2015
that women are simply not “hardwired” to play chess.
As J. Polgar argues, a healthier competitive scene is beneficial to raising the level of play, for all players! This is important both for 1. achieving a level of normalcy in people being or becoming passionate about the game of chess irrespective of their gender, similar to how education (in any field) should be pursuable on an equal footing without bias or restraint, and 2. it helps create role models and idols for girls finding out about the game. On the topic of absence of female world champions and idols, I further quote from the previous article:
The real reason behind the absence of a female world champion,
however, has less to do with crude biological reductionism than simple
statistical science. A recent study has argued that the dearth of
women in top chess tournaments is to be expected, given the gender
disparity in participation at all levels of the game.
The authors analysed the population of about 120,000 players active in
a single country, with a ratio of male to female participants of 16:1.
Their findings highlighted that 96% of the difference in ability
between genders could be explained by the fact that extreme values
from a large sample are likely to be far larger than those from a
small one. In other words, there have been more men represented at the
world championship because more men play chess. This, in turn, means
that a higher number are bound to reach the skill level of Carlsen and
If – then – we want to see a woman win the World Chess Championship,
we first must address the lack of female participation in the game.
The reasons behind this are complex, and likely manifold, but let us
focus here on just one: the lack of prominent female chess players.
There are no real female role models for young girls, even though
women have been playing chess for a really long time (the first
official Women’s World Chess Championship, for instance, was held in
1927). There are, of course, female players who have been recognised
for their outstanding skill, such as the Polgar sisters and the
current women’s number one, Hou Yifan. Yet these women aren’t assigned
the same level of importance within chess’s historical narrative as
men such as José Capablanca, Garry Kasparov, Fischer and Carlsen. As
all the “heroes” of chess are men, women are taught from an early age
to associate good chess with being male.
If we have any hope of addressing this, we need to raise the public
profile of female chess players. Alongside the news features on
Carlsen, we need to run one on Hou. We need to cover the Women’s World
Chess Championship with the same fervour as the “main” world
championship – or at the very least we need to, you know, actually
Some women have already made attempts to address the discrepancy in
media coverage and to raise the profile of female chess players. Take,
for instance, the Chilean chess player and musician Juga, who is
currently releasing music exploring her identity and experiences as a
woman in chess. By branching out, she is able to both boost her
reputation within the traditional community as well as drawing
attention to female players among audiences who have had less exposure
to the world of chess tournaments. It seems that this may be just the
time to bring about the endgame of male-dominated chess.
Addendum 2: Parallel with esports
As mentioned earlier, these issues are not inherent to the chess world. On a much larger scale, same issues of toxic behaviour towards female gamers and sexism permeate the online gaming world and its underlying industry.
To read more on the topic, below are a select of articles I recommend reading:
Addendum 3: important role of separated events
User Greg Martin makes an important point regarding the adverse effects of taking abrupt measures in abolishing female-only events. I quote the comment here (as comments might not be lasting in SE)
One point of disagreement (in a sea of things on which we definitely
agree): Polgar certainly is promoting participation in mixed
tournaments, but that is not the same as being against participation
in female-only tournaments, and I would suggest not dismissing them so
quickly. One of the characteristics of systemic sexism is that it
creates situations for which there is no great solution. Having
female-only events is not great, but not having them is also not great
(you have described many of the reasons why). Feeling included is a
very powerful aspect of the situation.