For what it's worth, I'm running Anach_NoIntro and Anach_NoQToQuit with Showtime/1.33 without problems.

I don't use Anach_CASSkins6x4 or Anach_CASDetails8x2, but I'd imagine there are issues with CAS UI mods and anything post-1.31, unless all the stuff regarding skintones etc. in 1.32 has been totally removed.

Anach_All_Buyable
Anach_CelebrityDifficulty
Anach_CelebSuePaparazzi

^ Twallan's ErrorTrap is picking up 1k+ script errors for me with these three, but I'm using all the service NPC tweaks (Mixologist, Repairman etc.), interaction tweaks, tweaks to bills and fees, and pregnancy tweaks without noticing any problems.