present subjunctive after "agree that"

Yes, but a native speaker would be unlikely to say or write that.

You cannot use the present plural (do not return) in that sentence.

Experts agree that any athlete who has concussion symptoms should not return to competition until they are fully resolved.

Or you could write

Experts recommend that any athlete who has concussion symptoms does not return to competition until they are fully resolved.

The present subjunctive ot the verb to do in all persons is "do."

I don't think that your second sentence is right. After some verbs or expressions -- such as agree that, recommend that, believe that, insist that...-- we have to use either "should + verb" or the bare infinitive which is in fact a present subjunctive.

Let's see what other people think about it.

Regards

It is right. After such words as agree, recommend, believe, insist, and 'that', we can use the appropriate tense (plural or singular) of a verb e.g.

Both my sisters agree that I do not have black hair.
I agree that dogs cannot fly.
My doctor recommends that I walk two kilometres every day.
He believes that his cats are sick.
My wife insists that he pays for the vacation.
I feared that my car was stolen.
I hope that my mother will call.

The subjunctive form is more formal.

See here

http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv201.shtml

Sorry, I meant:
Experts agree that any athlete who has concussion symptoms not return to competition until they are fully resolved.

That is 'correct'; it is also somewhat old fashioned and formal.