Instead of using adhesive to stick the LED strips, you can consider hot glue. Hot glue will quickly stick the strips into the surface without damaging the wall paint. However, this happens because this glue doesn't contain any strong chemicals that affect the paint's consistency.
On the other hand, several advanced pieces of equipment have been introduced to take care of the wall paint. Generally, people also avoid using nails to hang the strips. For them, damage-free adhesive hooks, drawing pins, wire suckers, and many more can be some of the best options to turn the LED strips without hampering the paint.