This article suggests that being on CBS All Access could afford the makers of Star Trek: Discovery more freedom in the language they use.
Of course, we know that in previous series, they sometimes avoid the issue by swearing in Klingon, Romulan, or French. And, of course there is this line from Generations:
But ignoring the movies, what exactly is the strongest profanity used in a Star Trek television show to date?
Clarification: Profanity is meant to include all taboo language, generally known as and/or including vulgarities, obscenities, swear words, slurs, curse words or cussing.