Instead, I believe there are projects which could appeal to rationalists across a wide range of the political spectrum. A couple I can think of are opposing the war on drugs and improving judicial systems. Any other suggestions?

You won't know whether you're "appeal[ing] to rationalists across a wide range of the political spectrum" unless you actually pursue that as a goal. Trying to find some "project(s) that obviously everyone will agree with if they are rational enough" is emphatically not a good way of doing this.

Trying to do away with political identity is very hard, and may well be impossible, if the literature on pervasive cognitive and systemic biases is any guide. When dealing with such contentious matters, it may be better to embrace existing identities to a limited extent, and focus on building "bridges" and "compromises" that people who hold on to a variety of identities can actually agree upon.