For example, take a Class A today and Class A from the 90's. Would the contemporary Class A be stronger because of the updates of opening theory or contemporary changes in chess play?
No. The vast majority of club level players still play like the vast majority of club level players always did. Changes in knowledge about chess mostly apply to high levels of play; the kind of mistakes class A players make were already known to be mistakes for ages, and opening theory doesn't help much if your opponent deviates from theory at move 5 anyway.
As evidence of this, see the paper "Intrinsic Chess Ratings" by Regan and Haworth, PDF. They analyzed the games of players of various rating ranges from various time periods with an engine, and found no significant difference in the mistake rate between games from the 70s and from the 2000s.
I don't think that there is a significant difference at that level. The main difference with chess 20 years ago is the use of computers and they are not extensively used by club players.
Also the advances in opening theory have been profited mostly by the top players (a club player normally doesn't know a lot of theory and doesn't memorize a lot of moves in depth of each variation).
Furthermore you can consider rating inflation and now the new K factors which make easy for a young player to improve his rating very rapidly in a good tournament.
In conclusion, I don't think that 1800-2000 players are stronger now than 20 years ago but I do think that top players are stronger now because of the facts mentioned above.
What do you mean by Class A? What do you mean by strength?
Do you mean talent (IQ, natural ability, genius, w/e) adjusted for time, resources, opening theory? That's probably a statistics, biology or cognitive science question. If the answer is yes, I don't see why that wouldn't hold true for math, basketball or singing.
If you mean talent unadjusted for such, then obviously today's top players are 'stronger'.
If you're talking about chess enthusiasts, probably not, but who's to say for sure? If you're talking about GM-level play eg Anand vs Morphy, definitely. If you're talking about NMs/IMs of today versus NMs/IMs (or their equivalents) of before, probably.
An analogy would be saying that Andrew Wiles is a 'stronger' mathematician than Taniyama, Leibniz or Euler. Of course he is, but that's mainly because of the works of the ones who came before him.
As Isaac Newton said:
Anyway, going back to chess
Bobby Fischer said (emphasis mine):
In chess so much depends on opening theory, so the champions before the last century did not know as much as I do and other players do about opening theory. So if you just brought them back from the dead they wouldn’t do well. They’d get bad openings. You cannot compare the playing strength, you can only talk about natural ability. Memorization is enormously powerful. Some kid of fourteen today, or even younger, could get an opening advantage against Capablanca, and especially against the players of the previous century, like Morphy and Steinitz. Maybe they would still be able to outplay the young kid of today. Or maybe not, because nowadays when you get the opening advantage not only do you get the opening advantage, you know how to play, they have so many examples of what to do from this position. It is really deadly, and that is why I don’t like chess any more.
Magnus Carlsen seems to think he could defeat Fischer or Tal, and why wouldn't he? He knows their games, has the Internet and is granted opening theory that Fischer, Tal and others had to discover themselves (eg 1 2)
As chess.com user fabelhaft put it (emphasis mine):
the main thing is that there is very little difference in talent between the best players of any time. The big difference is in the opportunisties the players had. Without professional coaching since childhood, modern opening theory, engine assistance, game databases, tournament circuits, Internet, etc, it was just impossible to play on the same level as those with all these advantages that were similarly talented.
There has been a lot of interesting points made here. I had been playing postal chess using books only and around 1988 it became clear that most of my opponents were using computers. I had some talent for chess growing up and I used it to play before I ever read a chess book. Of course having a lot of resources will make you play very good in the opening, often giving you an advantage over anybody that is not prepared the way you are. I would venture to say, talent for chess is not much different in the 2000s. People that have a simple interest in chess, play it just as entertainment are not much different than people 50 years ago with the same vision. Some people do try to study, and are only able to retain some much knowledge and can only work with facts in certain ways. At the higher level, I would guess because of all the materials available, the more talented players could develop into top players more quickly with dedication. I think you can see this in all sports. There is also a point where your talent seems to fade out a bit, like in your 40s. Top pool players, a game whose decisions are similar to chess, find themselves affected by age, health, and other factors. There are players in their 60s and beyond that are quite good, but they dedicated their every waking moment to their skill and remain good in most situations. For a champion, that is what it takes. 50 years ago, it was not possible to imagine the kinds of resources available today. If you owned 1000 chess books and had read a lot of it, you already had some advantage, even if you was not a top player. Players that have dedication and talent should be helped to reach their goals. Players that are playing to have a good time of just find interest in the game should be encouraged to enjoy it as much as they can take in. Better players should be able to recognize which players are their competition and act accordingly. I see and have experienced a bit too much ego dealing with people that had a stronger interest and investment that me. That hasn't changed much. I revel in the fact I am just a hack at pool, and I wear the fact I am out to have a good time and bang the balls around. I am just a cafe player, and although a lot of what I thought was weaker players now know the openings better, its just as easy to trick them into bad positions by bearing down on their game, even in good positions, since they are likely to make as many errors as I am.