Just don't ever, ever let them even see each other. First of all, you need to respect the fact that even seeing you cat will stress your beardies out terribly, as they are natural prey to wild felines and anything else that large. So even showing them to your cat can cause them enough emotional stress that they stop eating, we see it on here all the time. Secondly, we get at least a handful of sudden cat attacks on here a week, some are smaller wounds, some Lise legs, their tails, and eyes, and quite a few either get bitten through the skull or jaw and die instantly, and a large number are actually tortured by being clawed around for hours then either die from their injuries later on after suffering, or they die instantly from the stress causing a heart attack...And thirdly, and what most people don't know, is that ALL CATS have a bacteria in their saliva that is fatal to reptiles, and they have it not only in their mouths but all over their paws from them licking themselves. So a lot of beardies develop severe bacterial infections and die pretty quickly from just being near a cat, or having a cat jump up onto their enclosure and paw around...
Your beardies should be kept in a room with a latching door that is COMPLETELY OFF LIMITS TO YOUR CAT! A lot of people actually get locks for their beardie's enclosures because once their cat figures out where the tank is and no matter how high up they put it, the cat gets on top of the enclosure, knocks the lid off, and actually kills the beardie by either stressing it to death or batting it around the inside of the enclosure. They also have been known to grab the beardie out of their enclosures and kill them.
It's best to never ever let the cat see any of your beardie's tanks because once they see them they absolutely will not leave them alone. And I'll say this again, you must respect the fact that just the sight of your cat through the glass will cause your beardie a ton of stress that can result in any number of long-standing issues. Put your beardies in a room with a latching door that is 100% off-limits to your cat at all times, and if that doesn't work then get locking lids on their tanks. Cats and lizards do not mix in the wild nor in captivity, please don't think you can make it work out and they'll "be friends", because you'll no doubt end up with either a named beardie and a huge vet bill, or a dead beardie and regret.