plural gender-neutral pronoun referent for an impersonal antecedent

[bigzap05]

Which of the following are correct standard English? -

(1) Someone who enters a church should remove their hat/hats.

(2) Everyone who enters a church should remove their hat/hats.

(3) Upon entering a church, someone should remove their hat/hats.

(4) Upon entering a church, everyone should remove their hat/hats.

[Tdol]

1&3- I'd use the singular
2&4 Again I'd use the singular, but in British English, where we worry less than the Americans about singular and plural, the plural would be fine.

[mixolydian]

Since both everyone and someone are singular, I think the pronoun should be his.