No, Twitter has no bias against "mainstream political ideas". Their San Francisco urban chic politics are the very definition of today's "mainstream". Looking back over history, have mainstream political ideas always been the right ones, more or less? Or have mainstream political opinions frequently been pretty bad in retrospect?

The point of "free speech" is to be able to express opinions that aren't currently "mainstream" among fashionable thinkers. Free speech advocates aren't objecting to a single instance of some company expressing an opinion. That was just a "last straw", it seems. They are objecting to the tactics of Big Tech platforms in general, which use all sorts of deceitful methods to manipulate the visibility of arguments in order to influence the debate while pretending to be merely neutral platforms.