Birthday invitations typically don’t say bring a gift, much less specify a gift of money. It is like listing an admission charge. Emerson said “a gift, to be true, must be the flowing of the giver unto me,” but this invitation is a demand, one step away from panhandling.
A gift is something we aren’t entitled to.
There are two exceptions to the rule. At weddings, items are listed to help a couple set up a household, and at funerals, charitable contributions in lieu of flowers may be requested. These donations honour a final wish of the deceased, and extend their reach into the tangible world.
This barely teenage girl’s party is a fundraising campaign for a shopping spree. Aside from breaching etiquette, it is in poor taste. It encourages gifts to be ranked against each other; it destroys the pleasure of the giver in finding and selecting a gift; and most importantly, it lacks any sense of adult judgment.
We don’t freely give money to children. As an adult, you may feel this child needs a good book or something else to build the inner person, and that is your choice to make.
But if you follow the fiscal intent of the invitation, consider something like a small certificate of deposit which matures in five years. That’s about the time this girl should be starting college and begins to mature herself.