Are Cats Muktzah?

Question

We have heard (2nd hand) that recent poskim have permitted the handling of pets (such as a house cat) on Shabbat and Yom Tov and as such have deemed them as NON-MUKTZAH. This is a clear 180 degree about face from most earlier poskim who deem pets are completely Mutkzah. What is the current thinking on this matter?