Interesting views.
Some of the opinions are certainly an eye opener for me, others I could not help giggling at.
I have always perceived Mybb to have a strong leftist liberal leaning in most members, and that's true for the Mods as well (let's not touch on the Islamic / Palestinian bias). Bullying is another thing that appears to be well tolerated.
It just goes to show how different we all are, we do not all perceive life through the same lens.
You perceive MyBB to be left/liberal because you are so far right you consider the moderate right/centrists to be liberal. It is the same problem as the USA, where the "left" is considerably more conservative than much of the moderate right/centrists in, for example, Europe.
Your perception is thus because you do not objectively observe your beliefs as compared to the gestalt. Your personal "Overton window" doesn't allow you that view.
MyBB is moderate right/centrist in general. Some mods more right, some less. None are liberal. There is a small vocal community of actual left/liberals, but there is a much larger community of right and far right members.
Perhaps one reason for your perception is that it is mostly the far right who are silenced via bans, post deletions etc.
The liberal/left do not (well, I have had posts deleted, but no infractions for my contributions).
The reason for this is that, in my opinion, is twofold.
Firstly, a far right position tends to correlate with a lack of insight. Insight is useful when judging what can and cannot openly be said. Failure to understand that ends in a banning.
Secondly, the victim complex and fear of "the other" (especially communism, which for many equates to anything left of the moderate right) drives the conservatives to out-do each other in "owning the libs" - this usually ends in tears.