Is there any opinion that holds one may play or touch a pet on Shabbos (even though animals are normally muktzeh on Shabbos.) Specifically one that is meant for this purpose (to play with.) I heard recently that the Maharach Or Zaruah mentions such a thing. Is there any such opinion found?
It seems From the Igros Moshe OC 5:22:21 that pets are different and are not like other animals which are muktzah see the tshuvah inside it is very short.
It is not clear what R' Moshe held, as he is quoted elsewhere (Tiltulei Shabbo, p 119) as taking a stricter approach.
For other opinions see here: http://doseofhalacha.blogspot.co.uk/2014/07/pets-on-shabbos.html
R’ Moshe Feinstein (Igros Moshe 5:22:21) writes that small birds that are usually played with are not muktza, though elsewhere (Tiltulei Shabbo, p 119) is quoted as taking a stricter approach. As there is a machlokes as to whether playful pets are muktza, too, R’ Ovadia Yosef (Yabia Omer 5:26) writes that one should follow the majority of poskim and not move one’s pets. Nonetheless, as some poskim (Az Nidberu 8:36) are lenient, one shouldn't criticize those who do handle their pets on Shabbos.