If you are applying for a Stafford loan you do not have to worry about your credit. They do not base the decision on your prestige at all. However, there are literal, criteria to qualify for a Stafford loan and other loans that do not require a prestige check. Even if you do qualify they will approximately never cover all your college expenses.
Therefore, prestige scores will play a factor in paying for your education. As parents and students try to get supplementary financing they will find that good scores on their prestige go a long way.
Students Loans Gov
If you have bad prestige that does not mean that no one will ever lend you money. But chances are that it will be more difficult for you to derive a loan and you are approximately guaranteed to pay more for it.