If you feel pressure to do so, it is because there are conflicts that don't involve you, that others want you to have a stake in, for their own benefit. If there are two warring factions of graduate students, just don't join either one. The faculty don't really respect how well a student leads a faction of students in a squabble with other students, because that is just a source of trouble and irritation for them.
If the faculty use the students as proxies in their own conflicts, you probably don't want to be used that way. Imagine if you do a very good job at being used, then the professor will write you a recommendation--in which she cannot even mention that! If you put your energy into that kind of thing, you will be hated by those on the other side of the fight, but not respected by those who have used you. Being a good politician does not get you elected to the next level, hired by a department.
In an ideal department, the graduate students should not even know that there are politics. It shouldn't affect the students in any way. The faculty should put aside their differences in matters that directly affect any particular student. If students are asked to choose sides, they should still try to put their main energy into their work. The politically powerful advisor might not be the one who writes them the best recommendation and gets them the job.
If you quote Henry Kissinger to me on my blog, his famous aphorism that "academic politics is vicious because the stakes are so low," then think for a moment about his politics. I guess it is not vicious to bomb children in South-East Asia, or overthrow South American governments and put torturers in charge. Oh no. It is academia that is vicious! Because the stakes are so low!
In other words, the rewards are so small and tenuous and people's egos are so big. The resources are scarce. I get that. I would suggest that the stakes are very high, though. What is at stake is the future of an academic discipline, and hence of civilization itself. I'd rather quote Gandhi on Wester Civilization ("It would be a good idea." than Kissinger.