Dear Avira,
1. Minhag Yerushalayim has been contentious throughout history. It does not do anything besides pushing off change a few years. It couldn’t even prevent Shabbtai Tzvi from enacting whatever he fancied.
2. I’m not promoting Zionism. And I’m for sure not advising anyone to go up on the temple mount. But that beyond all the personal views, there is a bona fide halachic dispute on the matter. I know this second hand from someone trustworthy.
3. Politics based on Torah sounds like an oxymoron. And I hope you know that nobody is practicing it. A very small amount of askanim claim to be doing it. But nobody asks their opinion in any other area of Torah. And this includes those that have a small following.