Paul, who is no stranger to controversy, made the bizarre resolution on his podcast, ImPaulsive, after suggesting he could try "Fatal February", only drinking vodka and eating steak, following a dry and vegan January.
The conversation, with Kelvin Pena, known as "Brother Nature", started with Paul and his co-host Mike Majlak asking their guest for his resolutions.
But Paul then said: "We're vegan now, and we're sober.
"But February we are going to go the opposite.
"And then March... it's male-only March. We're going to attempt to go one way, swing, and then go back."
Producer Daniel Preda tweeted: "Logan Paul joking about being gay 'for one month' while countless LGBT+ around the world are killed & committing suicide for their sexuality, is disgusting. He continues to be an awful representation of the YouTube community & shows he truly has learned NOTHING over the last year.
"Perhaps for the month of March instead of baiting the gay community you can use your massive platform as a voice for those LGBT+ who have no voice and resort to suicide and self-harm. Just a suggestion @LoganPaul."
American charity Gay and Lesbian Alliance Against Defamation (GLAAD) tweeted about his comment, saying: "That's not how it works, @LoganPaul."
Paul then tweeted to GLAAD, saying: "very poor choice of words... my fault. let's get together and talk about it on my podcast next week?"
Last January, Paul was suspended from YouTube after videoing dead bodies in Japan's "suicide forest". He apologised afterwards and said he had intended to use it as in anti-suicide awareness.
The timing of this faux pas has prompted tweeters to question whether he "ever learns".