Hi Paige,
No it's not too rigid at all :) You own your business, and you need to be profitable at it, which involves pricing at the right level. There's a reason certain items are priced the way they are, and they're not meant to be affordable for literally everyone to buy. You sell luxurious bridal wear, so that's even more the case.
Also think of it this way, if you offer 5% off to someone, then that makes it unfair for the next person or previous person who buys/bought it at full price. If you're going to give a price break/have a small sale, then it makes sense to offer it to everyone.
Hope that helps, and lovely shop!