No.
There doesn't even have to be inappropriate conduct.
Correct.
Add sexual orientation to that list, in this state.
Correct. You also can quit for any reason.
It is an at-will employment state, not a fire-at-will state, like most of the country. It means that absent a contract, an employee can quit or be terminated for good cause or for no cause. Discrimination laws still apply.
Or if he stayed inside that day and was engaged in no conduct at all. He could have been fired just because someone else was in a bad mood that day (not that EMA is that type of place).
Source: I do this for a living.