Snoo
The Legend
You are, but those rules and regulations can't over-ride the local laws.
It's one thing to say "once you're in the queue you aren't allowed to have your mobile phone in your pocket", it's another to say "you must consent to a physical pat-down search by a ride-op". Of course, without the latter it renders the former somewhat useless, but I think legally there will be a line in the sand there. Then again, I'm no lawyer.
The Forth Amendment of the U.S. Constitution gives you an outline of search and seizure in the United States:
https://criminal.findlaw.com/criminal-rights/search-and-seizure-and-the-fourth-amendment.html
As such, given what Cedar Point is saying and not Ohio Revised as the Constitution reigns supreme over all state laws, they have the right to ask you to empty your pockets. They also have the right to remove you from the line or the park. However, they cannot search you without consent or reasonable suspicion of you breaking the law (bulging pockets, using your phone in line, etc). However, if they have no reasonable suspicion and are doing random pat downs, you can deny any official in the park that right without a warrant. Of course, denial means you get removed from line and/or the park.
Now as I am no lawyer as well and have only read up on this due to the nature of the world I live in being of African decent in America (several state laws outside of Ohio (Arizona and NYC I think?) trying to make it ok to perform random pat downs have been legally challenged in the courts as breaking the Forth Amendment), I wouldn't phone this home as fact but given the circumstances as well as the laws in the States, the above seems about right with what they can do.