You sentence is indeed ambiguous. You might be talking about meat from cats (kill a cat, eat it) or meat for cats (go shopping for a can of cat-food). In the terminal part of the sentence, "no matter what other people criticize" might mean people criticize things completely unrelated, like the Government's monetary policy or whether Ford's latest car is a good car. "People are always going to eat cats, whether or not Ford makes the next Bronco more economical" -> isnt really coherent
The following sentence better states that cats will always be killed and eaten whether people have criticisms of the process or not:
The custom of eating meat from cats will be maintaned forever, regardless of the criticisms of other people.