Of course everyone working at a social media company has an ideological bias, and that can come out in the product. But consider also that the latest censorship controversy creates negative PR, makes people leave the platform, attracts regulatory attention, and ultimately, hurts the company's profits. Content moderators are at least as worried about that as they are about making sure their ideological opponents aren't given a voice.
Social media companies are in the unenviable position of playing referee in the culture war, and like referees in any sport, they're going to constantly be criticized for doing it, right or wrong. These companies are global and universal, and there's no way they can satisfy all parties. Sometimes, the values of left and right, or Iran and the US, or Israel and Palestine, are just irreconcilable. You're better off just trying to avoid as much trouble as possible, and avoiding negative media attention.
Reddit is probably the most ham-fisted example of this approach. Their content moderation is pretty hands off, but as soon as any subreddit attracts negative attention, it's quarantined or banned, no matter if the controversy is justified or not. When Russia invaded Ukraine and Russia Is Bad Now, they just straight up banned /r/russia and any link to an .ru domain! That does nothing to address the conflict, but it does keep those NYT opinion pieces from showcasing Problematic Russian Bot Behavior on Reddit.
I'll note that I don't think this model fully explains moderation policies at Twitter or other social media sites. I genuinely believe moderation leans left due to an ideological monoculture (I've seen it first hand). But it's important to recognize the difficult situation social media sites are in.