I agree with Woodson on this. You're a professional, look like one.
"Professional"? So should "Professional" abstract painters wear a suit and tie, and only rock crew cuts? Who really cares? He died his hair, he should be able to do whatever he wants with his body it's his body.
It's not like JR got a middle finger tatoo on his forehead. Calm down old man. 
I think if it was coming from another coach then it probably would be a problem. Woodson is a no nonsense type of guy and I think they respect that out of him. That's like if Jordan Crawford decided to dye his hair orange and Doc (while he was still the coach) told him to change it, I bet Crawford would respect Doc enough to do it (whether it was a big deal or not).
I'm not old, I'm all about the image. I always want to present myself like a professional and look like one vs looking like a thug or a bum. I'm not saying he should wear suits and ties outside of the court, but something as simple as dying your hair? I mean, I don't take anyone who dyes their hair seriously.
And as the above said, this is coming from his own coach. He could choose to keep the dye for all I care, but I essentially take the coach as your manager. If you can't do something as simple as that request, then you're not a real professional. Don't forget, he's not only representing himself, he is also representing his team.
What image? 75% of the league is tatted up. Obviously you can't remove tats, but these guys should represent the country they live in. We live in America, freedom of speech/expression is the upmost important right we have. Judging a person because his hair is dyed, is real dumb to me. JR should be judged by his play, not his blonde hair.
Far too many people in this country (Boston especially), give kids who look a little different a weird look when they walk on or off the T or on the streets. WHO CARES? Maybe that kid is the next Steve Jobbs, next Jay-Z, maybe the next president.
Bottom line let the kid live. What's "acceptable" should be based off JR's behavior/play on the court not how he chooses to dye his hair.