I'm sure I'm going to have my head bitten off but here it goes.
I think you should do it for him. Think of it like wearing lingerie or getting a wax. You don't need to straighten you hair 80% of the time but if your getting dolled up for a date night, it's for him.
He loves you, he accepts you. He hasn't said that he's ending it unless you straighten your hair every day. All he's done is expressed a preference for your appearance. This is a hair site and many people are hyper sensitive when it comes to their hair but honestly I don't think it's that big of a deal.