From my experience Repulsion is a strange, situational ability, but at times can be a life-saver (particularly for your important ships).
Guardians out of the box are a very important unit to an Advent fleet. Their ability to absorb damage for a fleet (and the Mothership's ability to easily replenish multiple Guardians shields) allows them to dramatically increase a fleet's survivability. So by default the Advent fleet should have Guardians around, and researching Repulsion isn't that expensive (except in Crystal, which it is very expensive in).
Repulsion (a T5 ability) comes a couple tiers after you can technically get Guardians (although getting Guardians at T3 is usually not a wise move, Advent doesn't have great damage dealers this early and doing Guardians would just set you back). But by the time you have Guardians, and can opt to get Repulsion, you'll often be going up against significant numbers of Heavy Cruisers as your enemy's main source of damage.
Repulsion allows you to chose how and when to fight Heavy Cruisers, as the ability can force Heavy Cruisers out of their effective weapon range. Focus fire from Heavy Cruisers is usually the biggest killer of my good ships in long games, so being able to see an important Capital Ship is at 30% of it's health and dropping, and simply flinging enemies away to repair and regenerate can be quite the asset.
There are other situations where they can be employed, live covering retreats, stalling an enemy (with carriers they can be a real pain sometimes), or using them to delay an enemy's phase jump.
I wouldn't use Repulsion to try to guard a Carrier fleet (although technically two Halcyons using Telekinetic Push and Guardians using Repel could be quite a pain to combat) because although you could buy immunity from almost everything the enemy uses (except LRMs) your own strikecraft will be very easily neutralized by a relatively small, cheap amount of Flak. So sure, your fleet would be almost untouchable unless the enemy brought back their own LRMs, but you wouldn't be able to do much damage either while they go around trashing your worlds. I also wouldn't try to use it with an Illuminator fleet, since Illuminators are significantly outranged by the other LRMs and the Guardians wouldn't be able to protect themselves (bsesides the Illuminators damage and price issues).
Overall, it's not an ability you go in to battle always expecting to use (I never have it on Autocast) but in the situations where it has use it can be a lifesaver. Good to giving you breathing room and help prolong the lives of ships in trouble, alone not really a battle winner (like most of Advent toys) but with the right fleet has it's uses.
That's my take on the little guys.