In the Stonewall Dutch Defense, why does white play b3 and Ba3? Should I try to avoid it, or does it not matter?
1. Nf3 e6 2. d4 f5 3. g3 Nf6 4. Bg2 d5 5. O-O Bd6 6. b3 O-O 7. c4 c6 8. Ba3
The main reason is to exchange black's good bishop, and what would probably end up being white's bad bishop after a later e3. Another common way of doing this is Bg5xNf6. This also highlights black's dark-square weakness problem that he will have to watch out for for quite a while.
This exchange on a3 leaves black's other bad bishop on c8 more markedly bad, and the e5 square more weakened. After the exchange on a3, black can, and usually should, gain a tempo with Qe7, and the white Na3 will redirect to Nc2-e1-d4 (or sometimes via Nc2-b4-d3) to further control e5.
This scores well in my database at 67% for white, but many of the games are between players of disparate ratings. At the higher levels, it seems that black can hold equality, so I would say that if you are stronger, there is no need to avoid it, but if you are weaker against a good positional player, you might want to try to get in Qe7 earlier to make Ba3 harder, but white still has a4 then. I am not sure you can really, and totally avoid it if that is the plan white chooses.
In the pawn structure of the Stonewall Dutch the light squared bishop is the sick piece in black's position and the dark squared bishop is the star. If white can exchange the dark squared bishops then white already stands much better because of all the resulting weak dark squares in black's position, particularly e5.
Consequently it is a mistake for black to reply to 6. b3 with O-O allowing Ba3. Essential is Qe7 to prevent Ba3 and the subsequent trade of black's best piece. An early b6 is probably also important for black to allow the plan of a4 followed by Ba3 anyway by white to be answered by c5 blocking the exchange, possibly with Nbd7 to reinforce c5.
When you look at the position, you see a horrible light Bishop for Black, and you see a dark Bishop for White that doesn't have a whole lot to do, effectively. It's biting on the d-pawn, its 'natural prey' (the Black Knight on f6) cannot be effectively pinned, as the queen will be wanting to slide to e8 in this position anyway, so what's it going to do?
The idea of trying to force the exchange of Black's dark Bishop by effectively pinning it against the Rook is very attractive. It's more effective against the old stonewall lines, when the Bishop is on e7, because in this line Black can, effectively, get a free Queen move in by moving it to e7, forcing White into spending another tempo to achieve the aim.
It's a worthy aim, simply because of how mind-achingly bad Black's other Bishop is. But it's not a winning aim. Black can get some free development playing off the misplaced Knight on a3, and where's it going to go? It can't meaningfully get to b5, or really even c4. Back home to b1 or c2 aren't really attractive, and the only other choices are something like Qc1 or letting go of the tension in the center with c5. (It should be noted that the central tension is one of White's weapons against Black's buildup for a wing attack, so dropping it is kind of a big thing; I've been known to try and tease White into doing that with ...Qd6 simply because of how much stronger that makes an eventual ...e5. Depends on how you feel about double-edged positions whether you'll like that idea. White can get an interesting steamroller going on the Queenside if Black isn't paying attention.)
The best thing I can say for it is it can be effective against a lot of Dutch players who haven't spent time thinking the unthinkable: How do they attack without their chief weapon, the Kingside Bishop? Having to answer that question can throw a lot of Stonewall players off their game.
On the other hand, it does relieve one of the major issues with the Dutch, which is that Black has one more minor piece than they have room for, and that extra space can be handy as the pieces roll out. If Black has learned to be flexible, their game still has a lot of play in it (one reason why this isn't seen more often in high-end play).
If you're looking for a good anti-Dutch line, I've always felt the lines based around Nh3/Bf4 offer more than the b3/Ba3 ones. YMMV.