It's 39,000+change denominations including all the dangerous cults^†^ but not including non-denominational churches, who are typically too small and localized to be part of a ministry, but some are big enough but pretend to be small and non-denominational so as not to draw too much attention (because US law enforcement really doesn't want another Waco or Jonestown)

Some of these are actually extinct like the Shakers -- nope, we still have one Shaker village -- but between the 1970s and now, a lot of liberal / relaxed / left-leaning denominations faded into insignificance, correlating to a rising popular atheist movement. (Before the new atheists of the aughts and places on the usenet and the internet where atheist philosophy could spread, it was constrained to academics and scientists and hobbyist philosophers. Richard Dawkins was moved by the 9/11/2001 attacks -- enabled by radical religious suicide attackers -- to not just promote that atheism should be an acceptable norm, but we should challenge the rhetoric of churches, many of which were already a lot more politicized than they were supposed to be while retaining tax-exempt status.

My numbers come from the (defunct?) Ontario Consultants on Religious Tolerance in the aughts, which tried to catalog all the religions of the world and what they believed (and how they differed from their adjacent schisms).

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† In 23rd century parlance, when we say cult we usually mean an NRM (New Religious Movement) that is dangerous. There are plenty of NRMs that are not dangerous (that get cult status anyway and harassed by US law enforcement) and there are plenty of old religions (more than a century-plus) that are dangerous, but not regarded as cults.