The CM at Thunder Mountain made my DD take off her shoes (sandals w/ 1/4 inch sole!) to be measured. She was able to slide a business card between my daughters' head and the height marker, so DD couldn't ride.

I understand being cautious... but come on!
I know it sucks, but I appreciate Disney being cautious about ride safety. My niece wanted to go on Primevil Whirl in AK
sooooooooooooo bad, but after CM made her takes her shoes off, she didn't quite meet the height requirement. I felt bad for my niece, but would have felt worse if she had gotten hurt on the ride. I told her "Well, it's something to look forward to for next year!"
It isnt like the CM's are just trying to be mean...the safety rules are there for a reason. I know I wouldn't want to be the CM who let someone "slip" through who then got hurt.
All guests must wear shoes at
all times while in the parks. CMs do
NOT have the authority to ask a guest to remove their shoes at ANY TIME.
If a guest makes the height requirement in
unmodified shoes that are A) obviously the property of the guest and B) obviously the guest's
primary footwear, them the CMs must allow the child to ride the attraction. The top of the guest's head (NOT hair) must meet or exceed the bottom of the height check bar. If a card can be passed between the bar and the guest's head, they're too short.
That said: if I'm working an attraction with a height requirement and a guest is wearing shoes with an excessive sole or heel, then I'm going to err on the side of caution and get a manager to approve the guest (and notice that I'm saying Guest and not Child. Yes, I've had adult guests who did not meet the height requirement and were turned away. One was even a fellow CM).
I see parents who put their kids in boots/platforms to try to defeat the height checks all the time. And that's fine -- it's not my kid that's in danger -- but I seriously have to wonder: if the child is injured on the attraction, is the parent going to own up and say, "Yes, she was only 38 inches tall, and would never have been injured had she not gone on the ride but we put her in high heels?" Or are they going to say, "It's Disney's fault they let her ride! We're suing for one hundred billion dollars!"
If a CM asks you to remove your shoes (or your child's) for a height check, get their name and ask to speak to a manager immediately.
I also think that it's time this thread ended. This is going nowhere.
It's nice to have an opinion, isn't it?