I would say that they can be used in masculine or feminine form rather than they have to. In most cases, just saying "le chien" is normal/acceptable, espacially if you're talking about other's dog. I think you should still learn both. It is more natural tu say "ma chienne" if your dog is a female. "chienne" could mean bitch, but it wouldn't be in a normal sentence (people tend to yell those kind of words), and most of the time, it would be "espèce de chienne", so if you use "chienne", no one would take any offense. However, when it comes to cats, "chatte" can be more tricky, depending on who you are talking to, as it can be used to refer to female genitals...

Just to say that the answer of Aurelie is very good :) "Chatte" means female genitals, so if you are a girl and say "j'ai une chatte" I will laugh haha. But if you say "j'ai récupéré une petite chatte" for example it wont sound as female genitls ever. Chienne is absolutely not a problem because "j'ai une chienne" does not mean that you have female genitals or something.

Absolutely! Even if chienne means bitch in slang!