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It's a manifestation of Maslow's hierarchy of needs among a certain cohort that's allied with targets of discrimination and feeling politically cornered by the opposition's shift to the right. They see that the Overton window about certain types of discourse being mainstream has shifted because the opposition has moved further right -- both in terms of leadership and the views of the membership. They see radical positions working for their opponents, and escalate in turn.

There's a lack of nuance about whether they wish to push certain viewpoints underground and out of the mainstream, or if they wish to silence them altogether. Some probably don't care, which is troubling, but not altogether hard to understand. The effort is internally justified by invoking the 'paradox of tolerance', where they propose that the discourse of their opponents is fundamentally intolerant and presents a clear and present existential threat to society at large, and must be reactively suppressed for the health of diverse and open discourse to continue.