Should I allow this homebrew subclass?

Guys,

OP already did alterations on the subclass and posted here.

Kind of pointless to keep this discussion here.

There are a couple places where this is just too much compared to other subclasses. Except for maybe the slightly over the top dragon monk subclass, most monk subclasses tend to be reasonable in their limits. I think some of these need to be limited and some need to be modified to be better in tune with other monks.

Inner Light: Two cantrips, a skill, and a language is a lot. It would be fine if their other level 3 ability was somewhat subdued, but it is not. I would say one cantrip- besides, light and dancing lights somewhat overlap so it's not a huge sacrifice.

Celestial Aegis: Oh boy, where to begin. There's a lot here. Ten minutes this is a lot, and because of the design it's very good at level 3 and worthless at higher levels. I would recommend the following changes, though really as long as you pare it down it could be fine. First major problem is the wording of the first paragraph. The temporary hit points should be listed with other benefits. This is a classic homebrew blunder, and one that inexperienced players and DMs often let things slip because of- it looks like it has three effects, but actually has four. Let's talk about those effects.

Resistance to two (relatively rare, but also rarely resisted) damage types. Unless your player is an Aasimar, this is probably a very valuable feature, and if not, it's probably still good. Ten minutes of resistance is extremely good for a ten minute buff alone.

Additional damage (1dX based on martial damage per turn)- this reminds me of Hand of Harm, but without the ki point cost. I would nix this immediately here and maybe put it at the 11th level ability instead of the extra damage dice. Monk at level 3 is very good (relatively speaking) at damage, and that's when Flurry of Healing and Harm makes it "free" for Mercy monks.

Light- Inconsequential really, a minor benefit but one that over saturates given their additional cantrips.

Temporary Hit Points- I actually don't have a problem with this if the damage is moved to 11, but if it isn't, then it's giving the ability two mitigation factors (resistance and temporary hit points) and additional damage. The hit points are pretty minor at this level, but they do scale up and at higher levels they do too much for a bonus action ability that also gives you all these other benefits (and more at 11).

I would mode the damage bonus up to level 11, reduce the duration to one minute, and once all the wisdom uses are spent allow ki points to be spent to activate the ability (Monks should use ki, and I'm not ashamed for having that opinion).

Punitive Flash has a major "role" problem in my opinion. It is both a damage and a control option, and for some reason it's a Dexterity saving throw which is unusual for radiant/blindness effects. I would give it only one granted use per short rest, reduce it to Martial Arts + Wisdom mod (which makes it more viable at low levels), and remove the blindness and saving throw. This is an AoE defensive ability that *doesn't* target allies, with an effect that potentially gives advantage on attacks if targets fail their save. Stunning Strike already exists and is a nightmare for some DMs to balance, distributing that debuffing power in a reaction AoE is too strong. I would, however, if blindness is removed, let it be activated for 2 ki points. It's already a very good ability for damage since it doesn't target allies and it's a reaction. Compare it to Hellish Rebuke and while the damage falls off, as an AoE ability it has some unique uses, such as absolutely mincing low health enemies swarming the monk, and removing the saving throw makes it more relevant as a damage option.

Additionally, I would remove the option for the Celestial Aegis triggered effect to force the save at disadvantage for 2 ki points, for obvious reasons.

Radiant Soul is mostly fine, because I've made some changes to the earlier damage availability I would just change this to be "once per turn while your Celestial Aegis is active, you can deal extra radiant damage with a unarmed strike or weapon attack with a monk weapon equal to a roll of your martial arts die plus your wisdom modifier." This differentiates it from Hand of Harm a bit, and also makes it more independent of ki use. I would leave the temporary hit points feature as is.

Unstoppable Light is fine, I think. Level 17 abilities for monk are either very good or mediocre, and I think this is a good in-between. It adds some defense, but isn't broken to the point of making other level 17 abilities blush.

Anyway, those are my thoughts. As for whether I'd recommend allowing it, I would say that it depends on what other homebrew or other things you've allowed at the table. If there's other homebrew, it might be worth looking at that with a critical eye for balance and seeing if this seems like it would fit, or if it's a bit too much.