Hlaalu uses Armun Am, Redoran uses Gah-Julan, Telvanni employs mercenaries with odd helmets and unique shields....
Do Indoril soldiers and guards wear the ordinator armor? Or do they use their own unique type of bonemold?
Not unless they are also Ordinators.
You said it yourself. The bonemold armors of those Houses are not called Hlaalu Armor, Redoran Armor and Telvanni Armor, they are Armun Am, Gah-Julan, and whatever it is the Telvanni feel like wearing on any given day.
It was on the old website at one point that Indoril armor was in fact named so because of how many Ordinators actually come from House Indoril. So YES, Ordinator Armor IS associated with House Indoril but only as a nickname, and that doesn't give random Indorils the right to wear it. At one time, yes Great House Indoril did have much control over the Temple and the Ordinators, but I would find it hard to believe that they would use them for all their petty tasks. Not every Indoril city is a Holy City(though... many could be or could contain holy sites that would have Ordinator guards), I believe they would have regular non-Ordinator guards as well, and whatever armor they may wear, bonemold or not, it would not be Ordinator Armor(because only Ordinators may wear it). House politics and family guards would of course be handled by retainers like the rest of Dunmer society.
Indoril may have control over them, but there would certainly be limits to what they could have Ordinators do without coming up with a convenient reason having to do with the Tribunal or Imperial Law.