Hello! I'm a 3rd year veterinary student, and I can tell you it was tough deciding what schools to apply to. I believe the HSVMA (humane society veterinary medical association, part of HSUS) still has a chart out there of which vet schools do what to animals (i.e., if they get their animals from shelters, a breeding colony, animal parts from a slaughterhosue, donated, whatever, and if their procedures are terminal or invasive, etc). I used that to decide where I wanted to apply.
I ended up applying to Western, Davis, Michigan State, Penn, and Colorado (but programs might change, so it's worth checking into). Where you'd be comfortable depends on where you really draw the line - are you ok if the animals come from a breeding colony? Or no dogs and cats, but farm animals? Or if they use animals that were euthanized at a shelter or are going to be? It's a pretty personal decision, and the use of animals and what's ethical and what's not comes up for everyone in veterinary school, no matter where they stood on the issue before entering.
Western, at least when I entered school in 09, is the only school to only use animal cadavers that have been donated (like if your pet died at an animal hospital, you can will the body to go to a veterinary school) and practice on live animals is restricted to necessary procedures (someone comes in to get their dog vaccinated or spayed, not electing to do unnecessary things), and anything mildly invasive is very supervised. (... guess where I go to, hah).
Still, even if you don't directly participate in some of these things, it's not like when you go out and vaccinate or diagnose pregnancy in cows that these are someone's pets. Even if you're going to practice only on cats and dogs after graduation, you'll still be involved in the healthcare of animals used for animal industries during your time in vet school. I personally do not feel much responsibility over the situation - after all, the animals will be used for whatever purpose whether or not I'm there to take a temperature - but it can still be uncomfortable to be around at times. For instance, this year I had a 2-week rotation at an animal lab (our school requires everyone do it). While some of the regulations impressed me, it was overall very depressing. Like, I had a low opinion of lab animal stuff before, but I was still let down on a lot of things.

Anyway, the point is that no matter what, there are going to be things that will be uncomfortable or ethically challenging for anyone, animal rights-oriented or not. In that sense, you won't be alone in being uncomfortable with some of the classes and such. Even the very much not animal rights people have been uncomfortable (particularly with lab animal) and have had their beliefs challenged.

The lighter side is that, just by going to vet school, you'll be able to offer free or discounted services to some who can't afford it just because you're practicing or because many schools have their students work with shelters at some point. You can get involved with the RAVS program over the summer, where you go to rural areas (sometimes in the US, sometimes not) where you can provide free services for animals, such as spay and neuter. I know some people who have done it and LOVED it. Also, there are jobs at places like shelters where you can be involved with that type of thing. And while it might seem odd, many people who are concerned about animal welfare go into lab animal stuff after graduation, because lab animal vets are mainly involved with regulating the welfare of the animals at the facility, and can reject and stop experiments if they believe it compromises the welfare of the animals used. ... So it might suck for a while, but you can do a lot of good in the end.