Another idea not mentioned yet is to request that gifts be given to a charity in lieu. For example, setting up a Just Giving page.
The OP mentioned that this might seem crass; One way to make this less crass is to make it clear that not donating at all is perfectly fine.
You don't have to get me anything at all for my birthday this year but if you'd like to give something, charity donations to my preferred charity would be a welcome gift.