The negative connotations of 'flip flopper' are mostly based on the implicit assumption that the politician in question changed their[1] opinion for reasons of political expediency, i.e. for reasons more to do with polling data than new data actually pertinent to the issue at hand.
It is true that this makes it harder for conscientious politicians to legitimately change their mind, though.
The political flip-flopper is I think more scorned for flipping or trying to play both sides of issues that are more matters of principle than simply changing a position based on new evidence. I have much more respect for a politician who sticks to principles, even if I don't agree with them, than I do one who tries to have it both ways depending on who he's talking to.
("He" can be used with gender-neutral intent. I dislike using the plural "they" for this purpose.)
They is perfect for being gender neutral; the only other method I've seen is those weird journalist articles that randomly switch between him and her. They makes semantic sense and is explicitly gender neutral, I don't see what the problem is?
One can argue that he is technically neutral, but practically speaking the association is always male.
It is true that this makes it harder for conscientious politicians to legitimately change their mind, though.
[1]: they as singular gender-neutral pronoun FTW