How do I hang a soap dispenser on a textured tile wall?

Hi. If this is going to be a permanent fixture in your home, use construction glue. Put a good bit on the back and using painter's tape hang the dispenser. It may take an extra set of hands to hold and the other one tape. After it dries, remove the tape. Give it at least a good 48 hours dry time. Good luck!

Dbl sided auto detail adhesive comes in different sizes & clear

Can you hand it from the shower curtain rod somehow?

There's an adhesive on the market made by Lock Tite. Apply it on the back and hold it in place for a minute or two. Let it dry overnight. Next day apply bathroom caulk around the entire piece.