I was thinking that a charity might propose this to each party individually and get them to agree to it. But upon reflection, a better way would be to run a charity (or meta-charity) that works like this: when you donate money, you specify your affiliation, and the charity takes care of donating the difference to the appropriate party.

Perhaps it's not even necessary to specify a single neutral charity option. You give money to the meta-charity and specify your party affiliation and preferred charity. Then we donate the difference to the party's campaign fund as usual, and split up the remaining money between charities in proportion to how much was meant to be donated to each.