It says no smoking-not a problem. But it says no cats.  I have a dog but no cat.  And it won't let me PM them to make sure this ok. If I except the order and PM them about the dog and they can cancel the order right?  It was on the person's wish list and has been on hold for 2 days.  What should I do?

I'd check that it meets their conditions and send it.  If they have a problem with dogs, it would be in their conditions. 

I would also send the book without PMing the requester. She says "no cats", not "no dogs". Some people are highly allergic to cats, but not dogs!   BTW: thanks for being so careful; but send the book!!!

Yep!   Just because someone has a problem with cats doesn't mean they have any issues with dogs.  And since they took the time to write the condition, you can go ahead and send.

While my problems are not such that I have conditions, I'm allergic to cats & heavy smoke can trigger my asthma.  But dogs are just fine!

Send the book.

Ditto.  Send the book.

Triple ditto...send the book!

Quadruple ditto - send the book. Relax. No mention of dogs =  no condition.

The only time I alert someone of a potential issue when I'm not required to by PBS (thinking textbook highlighting here) is if I'm sending them an ex library book. And this is simply a courtesy and usually formed as an FYI, not a "do you still want it?" type thing.