It's a political party. If people that identify X vote for you, who identifies X and votes in a block with other people that identify X for matters that attract

It's a political party. If people that identify X vote for you, who identifies X and votes in a block with other people that identify X for matters that attract Identity X voters to said party... then you don't get to pull the No True Scotsman. You are the party of X, whether or not some arbitrary philosophy party X is supposed to uphold is consistent with the party's actions.