Yes, there are many cacti that you can safely touch even without gloves since, either they are without thorns (not all cacti have them) or they are small and curved, therefore harmless, or they can have large and pointed thorns but if touched gently they do not cause any damage.
Sometimes, I like to touch their thorns with my whole hand (gently, of course) to feel their protection.
The only plants that I never touch are the prickly pear, since (as I mentioned in the thread above) they have very small and tiny transparent thorns called "glochids" that if they come into contact with the skin they can hardly be removed, even with tweezers! In fact, I don't grow prickly pear very much, precisely for this reason.
Anyway, for all the other cacti there is absolutely no problem, since I keep pointed tweezers (needle, professional steel) so that if they accidentally get into the skin of my hand, I can easily remove them using a glasses lens,.... it's all about being prepared.