Yeah, if they're not going to let me have any say in matters that directly affect my ability to put food on the table for my family then I'm glad to walk. If your prospective manager isn't willing/able to go to bat for you on things like this it's a good bet they're not going to be willing/able to go to bat on lots of other things that matter while you are there. Not worth it.

Or, if they really are your only option at the moment, you can also sign with the intention of claiming you did so under duress if sued, but I'm not sure I'd be comfortable with that.