Ivy is a bit controversial. Eventually it does smother the tree, and it certainly increases the likelihood of the tree being brought down by strong winds. On the other hand it provides berries and shelter for wildlife.
Personally, I'm happy to cut a bit of ivy from living growth, as usually you will find that the growth is multiple, and anyway, it keeps it under control and increases the lifespan of the tree. Technically I suppose you need permission from the landowner, but I think people are more laid back about ivy than they would be if you felled the tree, say.
Cut it in moderation and it should be fine. You can get some great shapes from it, and it is once of those under-used resources that people tend to ignore. Try scraping off the fibrous 'gripping' threads that coat the surface, and using them as tinder. Abundant, and easy to collect.