Is the pronoun-antecedent agreement rule still valid?

I am asking the question because famous writers and literati I admire and respect are suddenly using sentence constructions that blatantly violate the rule.

An antecedent is, of course, the word that a pronoun refers to in a given sentence.

In the ff. sentence, "Everybody" is the antecedent being referred to by the pronoun "their."

Everybody is having their own version of fun.

I've always thought this construction to be wrong, but, for some reason, it is becoming accepted because respected writers are writing this way.

I wish to know the official stand of local academics and grammarians. Is such a construction a concession to the gay and lesbian community? Kindly email me your current best practice.

As of now, I stick to the ff. options:

If it's important to keep the antecedent singular, you have two options:

1. Everybody is having his or her own version of fun. (If the crowd is composed of males and females or if you are not sure.)

2. Everybody is having her own version of fun. (If the crowd is confirmed to be all-female.)

Everybody is having his own version of fun. (If the crowd is confirmed to be all-male.)

If not, then make the antecedent plural and then adjust accordingly. This also helps avoid accusations of sexism.

3. The people present are having their own versions of fun. (Is this grammatical now? Or should it be "The people are each having their own versions of fun."?)

Update: Thanks Splash for this link.