Humans assign rights, so yes, animals have some. For practical reasons they can't all have the same. Critters get more than varmin. Pests get few. Bacteria and germs probably none.
Domestic animals have certain rights in the Law, as do farm animals (UK). If they didn't then their would never be any prosecutions for cruelty. However, who are we to say that the life of a dog is more important than that of a rat? Why some eat the flesh of a cow pig and sheep but would not eat a horse or donkey. (well not intentionally, I think I've had horse or donkey meat in sausages in Spain)
If not we who says, then who are folk waiting for to tell us what to do ?
Food chains are part of nature. Life feeds on life. The predator gets to say what's prey.