Colleges using CSS Profile may or may not require the non-custodial parent finances (but most of the colleges commonly claimed to give good financial aid do). See https://profile.collegeboard.org/profile/ppi/participatingInstitutions.aspx – the third yes/no column indicates whether the non-custodial parent finances are required (but verify on the college’s own web site, since there have been mistakes or outdated information here before).
Colleges may also use their own financial aid forms; those that do may or may not require non-custodial parent information, or require it in some circumstances but not others.