As pointed out by several posts, the main problem is the fixer. But here there is a world of difference between film and paper. Paper absorbs chemicals into its very core, and requires prolonged washing to get rid of the chemicals. Film is plastic, and chemicals do not hang on to it. Just wash the negatives in running water for about 5-10 minutes and your films will outlast you. If you are paranoid, Ellery's suggestion of using hypo may be used. But there are lots and lots of professionals who do not bother with that.
Personally, I do not bother with hypo.