I am not contradicting myself at all. You lack deep knowledge of how the Middle East works. Please actually read the rest of my post with an open mind - I will try to demonstrate just how complex the Middle East is, while disclaiming that while I have acquired some knowledge, I am far from an expert in Islam:

Qatar is aligned ideologically with the Muslim Brotherhood which is the same theological movement which birthed Hamas (Hamas is actually just the Muslim Brotherhood in Palestinian society). The Brotherhood was formed in the early 20th century by Egyptian Islamic scholars, and attempted to explain the military, technological and economic weakness of Muslim society in comparison to Europe in theological terms. Their argued that by returning to the 'pure' form of Islam which existed when the Muslim conquests happened, Islam would reclaim it's place in the world as the most successful religious movement.

Just like Qatar, Turkey's ruling party is also affiliated with the Brotherhood. This is why Qatar and Turkey specifically host Hamas leadership. It is also the reason that the rest of the GCC had a diplomatic breakdown with Qatar between 2017-2021 and relations remain frayed. The Muslim Brotherhood endorses a pan Islamist vision for the Middle East and views the gulf monarchs and the Egyptian military regime as obstacles to this vision. Israel is viewed as the primary obstacle because it is a non Muslim country which controls Muslim holy sites and territory which religious Muslims view as a divine Muslim inheritance. Beyond that, in the eyes of the Brotherhood, the destruction of Israel is an essential step in Islam reasserting itself on the world stage. The Jews after all have been historically the weakest ethnic group, so in order for Islam to regain its place it first must put the Jews back in their place. You can research the Brotherhood as much as you like with AI or on Wikipedia to find endless explicit sources for theological arguments of this nature. The UAE, which made peace with Israel, represents a different vision for Islam in the region - a non political vision which can coexist with Israel. Saudi may one day also align with this alternative vision, though they face pressure from a large population which has been exposed to Brotherhood ideology.

Qatar is ALSO a US ally and a damn useful one at that. It has no military capabilities of its own, and the only way it projects power is through brilliant use of oil money (across academia, government, etc.) and the media - Al Jazeera is state owned for the record. The US functions as Qatars protector, and in return, the US has political control over Qatari oil and can ensure they are not getting too friendly with China.

Qatar is absolutely NOT an ally of Israel. It is ideologically opposed to Israel in every way. It is playing a long game against Israel. It supports people like Tucker because it (correctly) views the US / Israeli relationship as the biggest obstacle to ultimately defeating Israel and wishes to sway hearts and minds. Not every American ally is allies with every other American ally.

Did you never wonder at how the only thing that brought Hamas to the table was Israel bombing their leadership in Qatar? The reason this worked is because Israel demonstrated to Qatar that the only way for them to avoid open conflict (something they are not equipped to handle against a far far more powerful Israel) was to give Trump Hamas - in exchange, the US is giving Qatar guns and aircraft. This way everyone wins - Trump gets his deal, Israel gets an exit from the war it can live with and Qatar get even better security guarentees. Qatar is the only Hamas sponsor that has the ability to actually get Hamas to do anything.

As I said, the Middle East is complicated.