Excuse me, but what is exactly the problem with wine with regard of animal suffering? I know many vegetarians and some people strongly against animal suffering, and they all drink wine with no problem at all.
It depends on the wine. As you no doubt know, wine itself is pretty much just grapes. So I agree that one doesn't expect animal products to be in it. However, alcoholic (and other) beverages are typically purified or fined by the addition of another substance. Crushed eggshells, for instance, can be used to gather impurities from wine. Such a wine might be vegetarian (although vegetarians differ on their acceptance of eggs from battery hens), but would not be vegan. Charred bones can also be used as a fining agent. That wouldn't even be vegetarian. This sort of knowledge isn't something one discovers at once, but in bits and pieces through the years. I only recently learned that milk can be added to wine to remove damage inflicted to its taste caused by fires (apparently this was quite common after the Californian fires).
The fining process can be accomplished by wholly vegan methods. The typical reasoning for not using vegan methods is either an appeal to tradition or a reference to the cost of changing to another process. I have a nice bottle of white downstairs that I bought earlier, and which I intend to use (in part) to make a risotto. It's vegan. I have two bottles of red, bought for me by well-meaning acquaintances, which I regard as undrinkable, because I've checked them out, and learned that they aren't vegan.
EDIT:
Since the OP references the RCC, it seems odd to say 'stands for' and 'represents'. In Catholic theology, the wafer is the flesh, and the wine is the blood.
When this topic came up a while ago, my position was that I'd wait until I was dead, then ask God for some clarification on the issue. I'm still of that mind.