Diana went blonder and longer to please Charles. But when she wore her newly-grown-out hair up with a tiara at the opening of Parliament, and all cameras and headlines were about her new hairstyle. Apparently princess Margaret went nuclear and told poor Diana never to upstage the Queen again.
So it wasn’t the press who gave her crap about the hairstyle but apparently the royal family
I’ve read several times that the Queen was not impressed by her decision to show off her new hairstyle on that particular day, not that she had a new hairstyle in general. This is because the State Opening of Parliament is one of the main ceremonial duties that the Queen is constitutionally required to do.
By overshadowing the ceremony and it’s importance in the British political system, it drew attention away from the serious job the monarchy performs and just showed something trivial.
Diana, at this point, must have been aware of her media power, much the same as the Cambridge’s have now, yet she chose that day of all days, and several senior royals found that to be a little lacking in judgement. Whilst the Queen apparently didn’t say anything I’ve heard that Philip basically said how it was an irresponsible decision and, in no uncertain terms, that they weren’t impressed and then the issue was over.