This is true. For example Israel does not care about American fossil fuel industry. The fossil fuel industry does not care about Israel. Nor big chicken etc.

There are many different lobbies, often with completely different interests, which do not conflict with each other.

What Israel does control however is the American policy regarding Israel and the Middle East. That is where their lobbyists are.

The only time we see any pushback is for example when Saudi Arabia does not want America to bomb Iran because Iran will destroy the Saudi oil.