It may help (or then again, it may not - humor being subjective and all) if you reframe it in your mind as Archer and his compatriots being the butt of the jokes. In other words, you’re supposed to be laughing AT them, not with them. When Archer says something sexist or Mallory says something racist, it’s not because the writers are sexist or racist. It’s the writers poking fun at sexists and racists in the same way that the Colbert Report mocked conservatives - by embodying them and taking their schtick to the most absurd degree.
I adore the show, but it’s squarely in the category of humor (along with its spiritual progenitor, “Arrested Development”) where the characters are intentionally designed to be terrible people. The comedy comes from the way their personalities bounce off each other, the sharp-as-nails back and forth of the dialogue, the “Arrested”-style self-referentiality, and the superlative voice work. But it’s never an affirmation of the behavior of the characters. Even in the text of the show, it’s openly acknowledged that pretty much everyone at ISIS is a horrible human being.
By comparison, one of my other favorite comedies, “Bob’s Burgers,” is basically the complete opposite to “Archer” in tone - whereas “Archer” implicitly criticizes its leads at every turn, “Bob’s Burgers” is very much a celebration of its lovably strange characters (oddly enough, H. Jon Benjamin voices the lead character in that show, too). But despite their very disparate styles of humor, it’s very much possible to enjoy both shows - you just have to approach each show from the right angle.