The cross-contamination issue means more to some vegans than others. Some won't eat on non-vegan premises, some will accept that their food may have touched cheese at some stage, most are somewhere in the middle - direct contact is a problem, but one that can be taken care of through decent kitchen hygiene and separate chopping boards. The significance attached to one's view on this subject also varies from one vegan to another. Unfortunately, some vegans seem to see the issue as a cause to be arsey - and no, it isn't the 'militants' throwing a strop.
The blogger known as Fat Gay Vegan recently questioned a vegetarian cafe regarding whether their many vegan products were fried in the same oil as halloumi, having had a tip-off from a former member of staff. Now, as far as I'm concerned you take some risks going into a mainstream restaurant or cafe and have to take things on trust a little - be prepared to question and explain, and don't be scared to point out if something is 'off', but accept that in a new place you have to either be on the alert or take risks. I like to think, however, that a place which makes the effort to have specifically vegan items on the menu and label them clearly as such should make an equal effort to, well, actually make these things vegan. In particular, if there are a minimal number of dairy-based items around the kitchen, it's a pretty poor show if those get to contaminate everything else. The upshot of FGV's investigation strikes me as a happy one - the cafe realised that their existing arrangement wasn't working, and acquired a separate deep fryer to avoid the risk of harried staff at busy times dunking halloumi in whichever section of the existing one happened to have space.
Unfortunately, one commenter decided that asking these questions made FGV a 'douche'. Delightful. For some reason, not wanting animal products all over your food is unacceptable to some vegans. I can't help wondering whether they'd be happy making their sandwich on the same plate/board that a member of their own family had just been cutting cheese on (by which I mean actually cutting up a dairy product, as opposed to the other meaning of the term 'cutting the cheese'). And if so, why they'd be so averse to eating it themselves.
It has been suggested that asking questions about the vegan-ness of apparently vegan items in cafes, let alone about cross-contamination, might appear overly 'picky' or make veganism seem 'difficult' and less 'fun'. Mylene challenges that assumption here and again here, and I'm inclined to agree with her. Obviously be polite and keep a positive attitude - they may be able to make a vegan option, but if you're rude it might be contaminated in other ways! Eventually you will figure out which places have something decent and which don't, possibly with some trial and error.
On the question of making veganism look 'difficult' - I think it's a mistake to paint it as always being 'easy'. It's pretty easy for me at this stage, with a lot of practice and a knowledge base regarding where to eat in various cities. It isn't necessarily easy for a newbie - hence Vegan Grasshopper - but it will get easier as s/he develops more experience. Not bothering about whether your food is actually vegan is a step up from eating blatantly non-vegan things out of convenience or to be polite, but it isn't an effective or sustainable solution to teething problems.