I don't think this is true in the modern age. Countless non-established or up and coming comedians and adjacents have gotten fired for one-off remarks in old material or social media posts. If there's a constantly evolving list (which no one person on Earth is completely aware of in its entirety because of constant evolution) of "problematic" topics that will get you fired, all you will end up with is bad comedy.
More than 30 years after its release, Eddie Murphy was basically forced to apologize for Raw; undisputed one of the greatest standup specials by one of the greatest comedians of all-time. People were calling for a boycott of Netflix because of Chappelle and Seinfeld gets shit for his remarks all the time. If these were up-and-coming comedians, they would not have a career.