I can't answer definitively but possibly my experience is worth sharing here.
Thinking about food labelling, products may be labelled vegan and have a warning aimed at allergy sufferers along the lines of
produced in a facility that handles dairy products, eggs [...]
So, a product can be vegan if cross-contamination may have taken place. I am vegan for ethical reasons, as I believe is still the case for most people who follow a strictly vegan diet. Cross-contamination, rationally speaking, shouldn't be an issue, and I hear some vegans say they don't care about it at all.
Nonetheless, there seems to be a kind of disgust factor that varies from person to person. The other day I went to a stall selling French galettes, and ordered the vegan option listed on the menu, then saw them prepare it using the same equipment (with no cleaning in between) that they were using to prepare the non-veg foods. I ate the galette, but I didn't feel comfortable about it - I just felt that I couldn't waste good food (another, related ethical concern). I know other vegans feel the same way (having talked about this with many veg*ns over the years) to different degrees. For most, if the ware has been washed, then we feel OK (and in my culture and probably others, it would be rude to ask or complain about it as a guest, I think). But it's always extra nice for me to hear the kitchen is veg*n or "I used my veg-only saucepan", etc, and other people have said the same thing to me.
Besides the disgust factor, others may have a different approach to their dietary practices, such as religious commitments to avoid certain foods, as you mention, and I can't answer for those, although such concerns might be a factor for some of the vegans I've talked to who say they feel better knowing that separate equipment has been used.