The amount of true belief varies from company to company, but largely the answer is a firm "No". BigTech definitely politically leans towards the left, but that is due to decades of slow infestation. Still, at the very top, they largely don't give a fuck. Why they signed on is a bit complicated, but I'll simplify it a bit. Put simply then, the Left was willing to promise them power, and seemed poised to be able to make good on that. The right was in remission, largely run by RINOs and almost entirely controlled opposition. Hillary was lined up right after Obama and everyone hated Bush. The left was ascendant to true Single-Party status. So, when the left made overtures to them about providing them near-limitless power they signed on and slowly but surely their policies more and more favoured the left.
And then the U.S. populace threw a giant orange Molotov at the establishment.
Trump had some interesting effects that rippled out from his election. He kinda took everything that was slowly going wrong and then just made it -worse-. BigTech was actually the most insulated from this, but the problem was that Trump made a brand new problem. With Obama out, they suddenly had to actively do something and the Democrats kept putting more and more pressure on them to make the Right miserable. Until then, they could sorta pretend to be non-partisan but now they were being forced into completely alienating one side. Still, with no real way out of it and the promise of a Cabal which would set everything back to normal they did it. They did it, and regretted it.
Yes, they got Trump out. Yes, they had a pivotal role in it. But things didn't return to normal, they only got worse.