Why not 5.Bd2 in the French Defense: Exchange Variation? After the initial moves of the French Defense: Exchange Variation, my opponent played 4.Bb4+. I followed with 5.Bd2, but after analyzing it, I saw that it is not in the master games opening on chess.com and 5.c3 and 5.Nc3 are considered better moves.
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1. e4 e6 2. Nf3 d5 3. exd5 exd5 4. d4 Bb4+ 5. Bd2

It looks like the most natural move to me, because:

It forces the bishop away or to take my bishop which I can recapture with my knight, therefore developing it if he decides to take
c3 looks like a less natural move because although it pushes back the bishop, it prevents my knight from developing on c3 in the future
Nc3 looks like a less natural move because it pins the knight to the king, and if he takes my knight, he gets my pawns double stacked on the c file, which I always have thought you should try to prevent

So, why the move is weaker?
It appears to be 4...Bb4+ that's the unusual move here. The chess.com database only shows one game with it, and that's the game that continued with 5.c3. When you have the position after Bb4+ on the board and it shows 5.Nc3 with a bunch of games, it's actually showing games that transposed into that position - the Nc3 was played earlier in the game.
Given that there's only one actual game in the database with Bb4+, there very well may be nothing wrong with Bd2. It hasn't been played simply because the position almost never came up.