I think it is probably more true that social media companies have the ability to cause people to think in certain ways. During covid early days, there was a lot of propaganda surrounding covid, and social media was censoring posts that did not fit a particular narrative.
Many social media companies are trying to do similar things regarding gender, however, what they are pushing is just too ridiculous for most reasonable people to accept.
It's not social media companies that cause people to think in certain ways; they'e simply the delivery mechanism. But obviously social media
can be exploited by people/companies/nations to cause people to think in certain ways.
Facebook/Twitter etc don't have an incentive to promote any particular narrative, other than 'Facebook/Twitter is great'. Censoring tends to occur when social media companies decide that they need to do something because if they don't, it will reflect badly on them, and they could get into legal trouble or (worse) lose revenue. Censoring Trump (which is I think what you're alluding to) was done entirely out of self-interest, I don't imagine they give a f*ck about Rep/Dem etc, they're interested only in themselves as a company and how their actions or inaction affect their profits.
As regards Covid, they probably don't want to be seen to be promoting the view that people should be injecting themselves with bleach or exposing their internal organs to the healing power of sunshine. That could reflect kind of badly on them.
As regards gender, if social media companies appear to be
pushing anything, then I'd suspect again it's out of self-interest, and not wanting to be accused of being anti- anything.
It's all self-interest, nothing more sinister than that.