I've never met any vegans who would be bothered by this sort of thing. I wouldn't want a leather sofa in my house, but I'm not going to be ridiculously unsociable and refuse to sit on a leather sofa. These extreme cases don't really tell you a lot about what's important and positive about veganism.
I wouldn't, but from having done a little voluntary work for the BUAV I know that it's an extremely complex issue. I still use toiletries that are probably tested on animals. So what? I already do a lot that I'm happy and proud about. There's no need to be absolutist or fall apart from trying to get too many things right. I'll simply wait for more people to become vegan, as that will mean that the more remote objectives (for me--for some people, campaigning against animal experimentation is their number one priority, whereas I'm more concerned with nutrition) can be achieved.
It depends on what you mean. As I mentioned above, I don't have a problem if something contains trace animal products owing to being produced in the same factory. I think that's vegan--a pragmatic vegan, perhaps, but vegan. Unless someone has done a really sloppy job of cleaning machinery, it's not going to make a great deal of difference.
On the other hand, if someone said, for instance, that they would eat a dish because it only contained a tiny amount of meat (perhaps anchovies) as part of the recip,e then, no, that wouldn't be vegan.
Then you'd never be able to taste the delights of Worcestershire Sauce :-(
Then you'd never be able to taste the delights of Worcestershire Sauce :-(