Ok, so I think talking about broken Illuminators and saying how you beat them is a dead horse. The entire community seems to be behind it, so I figured I'd go into the best answers you've got for repulse, the OTHER thing that needs fixing.
Here's my take on the best current options to fight off someone abusing repulse, and it's in order from most effective to least effective.
TEC:
Option 1: LRMS (and Akkan with third abiliity that gives extra range if possible)
LRMS are the #1 answer because their range is huge and they can still shoot at the Guardian EVEN from the fringes of the repulse "bubble". They get a 75% damage multipliers, or -25% for the arithmatically challenged. Sadly, that's the best multiplier that any ship that can actually shoot at the Guardian gets. Problem with this answer is that Guardians are always used with Illums and Illums tear LRMS to shreds.
Option 2: Dunov's EMP Charge
I think this is one of the better answer for TEC simply becausing taking away the antimatter of a Guardian is the most direct way to stop repulse. The problem is the ability's range is rather small, but the ability has a HUGE area of effect, so aim at something near the Guardian and you will sap antimatter from your opponents cluster of guardians HOPEFULLY stopping repulse sooner than your Advent adversary was thinking you would.
Option 3: "Spam" Kols that are supported by Hoshikos, Dunovs, Akkan, etc.
This works if you have the time to do it. Kols can reach guardians with their beam attack on the front, and the autocannons will attack the Illums that get too close. If you have say 4-6 Kols it's really hard for your repulse abuser to pick out one target to take down. This strat is very expensive though.
Option 4: Strikecraft
I have this lower on the list because even though Strikecraft are immune to repulse, they (fighters & bombers) get 50% damage multipliers against Guardians. That's just bad. When you consider how strong flak are now and the fact that a halcyon will completely stop this tactic, it's just not a good option.
Option 5: Cobalts with Sabatoge Reactor
The cobalt gets an ability where it will deal 100 damage to any frigate that tries to use an ability AND disable that ships abilities. Sound great, except Illums are always there and will completely tear cobalts to shreds. No question.
Option 6: Akkan with Ion bolt
You fire ion bolt on a small scale to stop the actual guardian that's doing repulse. Only works if your opponent has a few and even then on a VERY small scale. At best a stall.
Option 7: Missile Barrage
Repulse pushes the Marza away, but if you can somehow get it close enough, it'll work. I have it this low because repulse will push the Marza away while it's doing MB so the ability loses its strength.
Advent:
Option 1: Fight rock with rock
Make Illums, guards, and do repulse yourself.
Option 2: Subjagators
Advent has a second support frig called the Subjagator. It's first ability is to pick an enemy target and disable it for 40 seconds. Completely. The range is long enough to reach Guardians. It's just expensive to get, and expensive to lose.
Option 3: Disciples with antimatter steal
Pretty much the same arguement as any LF. Great if there are no Illums.
Option 4: Strikecraft
If there are no flak/Halcyon, it'll work, but same problem as TEC.
Option 5: Reverie on the Revalation
Like ion bolt. Works on small scale. Takes ship out of game for 40 seconds or so.
Option 6: Domination on the Rapture Capital Ship
It's a level 6 ability, so it's tough to get. It's nasty though. You steal the ship from your enemy permanently. Just tough to get and long refresh time
Vasari:
Option 1: Assailants
Their range is huge and have phase missiles. Problem is if your opponent has Illums, you're screwed.
Option 2: Nanite Bomb on the Egg
If you get near enough between repulse the egg does enough damage to the hull to take it out.
Option 3: Starbases(Courtesy of JJ)
Since it can move and repulse doesn't affect it, this is great. The drawback is the starbase is restricted to one gravity well.
Option 4: Skirmishers with their ability
Upps antimatter cost by 2X and ups refresh rate of ability by 2X. It's a LF, so it'll die to Illums.
Option 5: Subverters
If you can get near your opponent with them, yeah, but normally you can't.
Option 6: Strikecraft
Same as before with Advent and TEC.