Is it muktze for others to touch my pet on Shabbos?
According to most poskim pets are muktza even if they are meant to be played with. The reason live animals are muktza is because we are not allowed to use them in any way, such as riding them or use them, and even though pets are meant to be played with, nevertheless. Essentially, there isn’t any difference between the owner of the pet of the owners friends. Therefore your friends should regard your pets as muktza.
Shulchan Aruch Horav O:CH 308-78, B’tzel Hachochma 5-33, Be’er Moshe 2-28, Yabia Omer 5 O:CH 26, Shmiras Shabbos Khilchoso 27-25, 20 ftnt. 171, Orchos Shabbos 19-124, Tiltulei Shabbos pg. 118, Hilchos Muktza ( R’ S. B. Cohen) pg. 225.