We don’t see the proceedings of the Council, but we do see who visits Ahsoka after she is kicked out. Obi-Wan is not one of those people. A vote, especially when you are outnumbered and know it, doesn’t mean a whole hell of a lot in comparison to visiting a friend, comforting them, and fighting to find the true killer.
He didn’t do any of that, so I don’t particularly care what he voted. He didn’t help exonerate Ahsoka and he never visited her and he never apologized before her name was cleared. Who doesn’t love the support and apology of someone who waited around for others to actually help you first?
And you know what? I’m on board with Obi-Wan feeling guilty about this. I’m not saying he looks happy in this gif. I’m saying that he, like everyone on the Council, prioritized THE COUNCIL over the individual needs of a Jedi. Because that’s what Jedi DO. But if we are going to turn around and make it about the relationships that Ahsoka had with these men – and yeah, Plo, you’re not off the hook – then what these episodes tell us is that those relationship were not, and could never be, priorities to Obi-Wan or Plo. It is Anakin’s downfall that he is the kind of person who would never put the Order before a relationship, right or wrong. That Obi-Wan and Plo would prioritize the Order (it’s authority and it’s current theology), even when wrong, is the downfall of those relationships.
There is a cost to being a good Jedi and there is no wiggle room. Obi-Wan knows he can’t support Ahsoka and be a good Jedi. Justice alone should be enough, an apology should be enough, and if it’s not – well, remember who it is on Utapau who blamed Ahsoka by saying emotion clouded her judgment? Yep. That was Obi-Wan.