We should respect animals the way we respect people.
We should respect animals just the same as we respect people.
Animals should be treated with the same respect as people.
こんにちは。
さまざまな言い方ができると思いますが、下記のような英語表現はいかがでしょうか:
・We should respect animals the way we respect people.
・We should respect animals just the same as we respect people.
・Animals should be treated with the same respect as people.
ご提案いただいた英文で問題なく通じると思います。
ぜひ参考にしてください。