It depends on the school. None of them can require you to list it in order to get federal loans since the schools themselves don't allocate federal loans, and the government has decided that you don't need to list it. However, most schools want you to list parental information on the FAFSA in order to qualify for institutional grants.
No, it won't affect your loans, as long as you're talking about federal. The government is the entity that issues federal loans (not the schools), and the government doesn't consider parental information when giving out federal loans.