I am surprised how many people here are up in arms over a prayer or an anthem before a meet. Prayers are words and songs are music and words. Either the words or music has meaning for you or they do not. But they cannot hurt you.
I get it that people feel peer pressured- but that happens in many areas of one's life and to call that force is disrespectful to people who actually do live under the threat of force. There are places on this earth where people really are forced to comply even in private with the rules of a state religion or constantly show subjugation and obedience to a government or leader and will be put in jail or killed for not complying. So please, think about what you are saying when you say you are being forced to stand for the anthem. If you think your gym is going to take it out on your daughter if you do not want to politely stand for 3 minutes to hear the anthem of your country played or a prayer said, then the problem is with your gym, not the country.
As far as "allowing" prayer. We have this thing called freedom of religion in America, it is in the first amendment - and that first part is no accident.
That means if you want to pray, even out loud, even with other people around, even if you are the official at a meet, you have the legal right to pray, to lead a prayer, and frankly to ask others to pray. Yes, asking (as opposed to forcing) people to do something is not a crime. Interpretations by the courts of the first amendment over the years has taken the right to pray away when the prayer is connected to a government entity- this is why you cannot (officially) pray in (public) school- as one example.
But the meets I have been to have never been in a government facility. They are held in and by private businesses - gyms or spaces rented by gyms so they can run a meet. So I am pretty sure(?) prayer in that context is legally ok, and may I add that while I myself only pray silently or privately, and am not into public prayer myself, one thing I pray about is how thankful I am to live in a country with the freedoms we have.
Now that said, we have not once been to a meet where there was an official or unofficial prayer before the meet or at any other time. I imagine prayer at a meet is actually quite uncommon overall.
But there is always a recorded or performed version of the national anthem, and yes, traditionally, those who wish to and can, stand and face the flag. As far as hands- I was not sure so I looked it up.
Currently, it appears the protocol is hand over heart for everyone except people in uniform. They are supposed to salute. Veterans and military service members NOT in uniform may either salute or put hands over hearts. (this is a somewhat recent change, it used to be that they were not to salute if not in uniform.) And talking during the anthem is considered disrespectful. But all of this is voluntary, you do understand.
The Stars and Stripes is a symbol of the country, the United States of America. Not of the military, not of the president, not of the government, not of the Olympic team etc-- although of course depending on the context, it could represent some specific entity as well. So if someone wants to say, 'I am standing for the anthem to support the military,' it is not incorrect exactly so much as incomplete. Country flags (and anthems) symbolize the country they represent.
