I just wouldn't do it.
As Popeye would say, "I am what I am and that's all that I am".

Plenty of clients request certain outfits or articles of clothing for an appointment. I've been asked to wear everything from a lingerie in a specific shade of lavender to "heels no higher than 2 inches".  Frankly, I'd be thrilled if a client offered to pay for a specific style that they'd like to see me in.  It would certainly save me a few bucks lol.

But, while asking you to change your hair color (or anything else that isn't easily reversible) isn't exactly *offensive*, I do find it incredibly presumptuous. Our looks are a large part of our marketing, and drastic change of hairstyle could lead to clients feeling mislead when we don't look like our photo. And honestly, a client who felt entitled to even request something like that of me would make me incredibly uncomfortable.  There's a weird power dynamic when you give a client that much control over how you look.  

Now if it's just a matter of you wanting to mix things up, or you just go crazy for redheads when your provider's a brunette-- why not offer to buy her a wig?  You'll get exactly what you're looking for, and she doesn't have to commit to *your* idea of what she should look like.