Are dogs allowed?

Yes. Would caution taking the dogs if you plan to complete the hike. There are a couple short but steep inclines that may be difficult with a dog on a leash

Dogs are not allowed! There are signs posted and there is a fine if you have them

Yes on a leash

Last time I was there, no dogs allowed. Both BLM.gov and Newmexico.org sites for Kasha Katuwe Tent Rocks still state this. https://www.blm.gov/visit/kktr