Well, as I said, playing between 2 factions (or more) is not an easy task. You will be shunned by both of the radical parts of them. But you can also get relations outside of your faction, which is often not the case a lot when you play a radical one or sometimes a simple conservative. If you play it well, I can assure you it is rewarding. I know it, my character is speaking with amarrians, mataris, gallenteans... And is also shunned by all their radicals. Us playing amarrian liberals are trying to reform the Empire from the inside, fighting against slavery as much as the freedom fighters are doing it, but on a different perspective with different means. We are shunned by the matari radicals because they do not want to admit that our characters are doing it, and this is what we usually expect from radicals when you come to propose different answers, even if they are working for similar goals. If you do it well you can generally get in good relations with the people just next to your position on the political roster (on both sides).
And I do think that you can definitly be a tribalist while being part of the Angels. Look at the IGS thread asking to people to explain what they thought tribalism was about. As much different answers as different characters involved. Miz IC point is valid, you harm the tribes by helping the Cartel. You can also help some tribes when helping the Cartel while you would harm them by helping the Republic destroying the Cartel, those tribes depending on its economy, help, dirty funding, black market, etc. The example presented above about the system invaded by the Cartel where the local population happily joined them (at first) is a proof of that. While still harming other tribes by supporting the cartel, they also help their own tribes. You can basically hate the standard republican tribe and work for a more outlaw tribe model. Tribal structures are totally independant of the political affiliation, be it Republic or Angel. It reminds me a roleplayer I like on the IGS, playing a thukker leader, just caring for his own people and tribe, and not giving the slighiest fuck about the rest of the cluster.
When you explain that Nikita mostly cares about Utopia, then it is totally legitimate for her to think that the Republic is the enemy. That the tribes supporting it are at least indirect enemies. Who said all the tribes were always all sugar between each other ? Remember the difficulties for the thukkers to get accepted, or even the starkmanir/nefantars. Remember the differences of ideologies between them. And also, the most important part : remember that in the core PF of old, the Matari people is described to be the most numerous of the cluster, AND that a lot of them live outside of the Republic, for a good part as shady wanderers (like ronins), unscrupulous people or pirates.
Or you can play a character that does not give a fuck about tribes, but cares enough for the matari people living in the Cartel (Utopia in particular) to fight for them.