Legal Question in Real Estate Law in California

Yes

It is not a crime to do so, and you would have a hard time showing in a civil action that they did anything wrong, so,

yes. they are allowed.

In an hour of researching the topic of stray or trespassing cats on WestLaw, I could not find any authority for either a "yes" or "no" answer to your question. If Mr. McCormick knows of a statute or any case law expressly or impliedly authorizing this, which admittedly may exist, I at least could not locate it. There are indeed laws relating to stray dogs and "estray" livestock, but cats are not within the applicable case law or statute, by definition. The cat's entry and presence in the neighbor's yard is indeed a trespass, but the right to self-help to correct a trespass is quite limited, and the more general law requires a victim of trespass to apply to a court for relief rather than resort to self-help. It is interesting to note that if the animal were, for example, a bobcat or a fox, catching it would be illegal trapping. So, for me, the answer is "maybe, maybe not."