A unit with a face-up order token does not flip it over until the end of it's activation.

If a situation arises during it's activation (such as friendly standby vs enemy standby), can a unit that started was issued an order (ie: has a face-up token) use Fire Support?

This seems clearly unintended, but the only place the rules suggest it cannot be done is that once the Fire Support is *completed*, that unit (which is in the middle of its activation) that unit cannot be activated.

To be clear, my intent here is that the wording is cleaned up a little or that someone points out a better passage in the rules that prevents this.

Its exceedingly rare to have an opponent's standby trigger a friendly standby, why didn’t the unit that took the second standby just shoot instead? Why didn’t the first unit with standby not trigger it when the second unit moved into range? You would have to have an opponent move into range, not attack and take a standby token, all the while your unit that already has the standby token would not use theirs. Seems almost impossibly unlikely to happen.

I do see what you are saying though as if you could create this exact magical situation you could potentially move, trigger both standbys, adding fire support to your friendly unit, then because you haven't attacked as an action you would be free to perform an attack action as well. Perhaps the developers saw this but thought this exact scenario was so unlikely that they didn't feel the need to worry about it?

I think as you say its clearly not intended to happen and at some point the RRG will be updated so that to use fire support a unit must have the fire support keyword, a face-up order token and has not yet activated this turn.