Red v White wine in cooking with a stomach issue
The way red wine is produced vs the way white wine is produced might give you some insight.

Red wine is produced from red grapes where the "mosto" (grape juice) macerates together with the skin of the grapes. This releases the typical red pigments and tannins.

White wine is produced from red or white grapes where the mosto does not usually macerate. If it's from white grapes, it can macerate with the skin.

This means the wine has less tannins (and pigments).

Basically, the only difference between the wines is the amount of tannins.

For some info about marinating meat in red wine, this post is interesting. Hint: it doesn't do much.