If they attach conditions to their wedding funding (which is their right to do), you will have to make a choice about how to proceed.
Your obligation is to realize that they have some leverage, should they choose to use it. Their obligation is to realize that this is supposed to be your wedding. Accepting their money may cost you some autonomy.
Parents paying for the wedding is a gift and they have no right to tell their adult daughter who she can and cannot invite just because they are footing the bill.