My thoughts on this are that the only sensible approach is to allow prayer. That would even go for public schools, where I think excluding prayer is dumb- stupid really.
If people have culture in their lives, which they obviously do, then it's senseless to try and force it out of people.
That's by view as a Christian person, and would probably be my view as a non-Christian.
But that does not mean I think that the prayer needs to be vocalized either, nor limited to just Christians.
Suppose there was a person who was mute, and could not speak. We would be foolish to say that such a person could not pray. Because if they can think in a language, they can pray in a language. Therefore they can pray silently and effectively in a language. And if they can do it, then anybody can do it.
And because of this, nobody really can stop prayer at a function, because they would never know if it was silently done. And I seriously doubt that God is going to frown on a genuine silent prayer of thankfulness. So because prayer cannot be stopped in that manner, that's why it's pointless to prevent it. At least completely.
It would more sense to encourage people to take a moment to pray if they like, in whatever fashion, silently.
Also, some people say that prayer, if spoken, makes them feel uncomfortable. Well, I'm certain many of those people speak things in their normal conversation that could be pretty awkward to others too.
I see two problems with situations like this.
1. The non-religious or anti-religious foolishly hoping to sterilize cultures from day to day living.
2. Christians or other religious people acting in a mechanical legalistic fashion as if they must do the same thing, the same way, every time, without adapting or modifying their actions.