This is giving me some vibes of "without religion people be murdering each other".
There's no moral conflict in eating meat and not murdering humans, eating meat and refusing to hurt animals other ways, or even eating only some animals and not anothers.
I have well developed morals about the animal thing. And they are not based in giving animals rights. I don't consider animals as having rights like humans. What I consider, on the other hand, is humans having the duty not to be cruel. So hurting animals (or even plants) for no reason is cruelty thus is wrong. This allows for the hurt of other living beings without cruel intentions, and sits pretty good with a lot of different situations and dilemmas on what's right and what's wrong.