I agree with H-K-J - the cave needs to be clean, utensils, pots, thermometer, cheese moulds and cloths, as well as draining board -all sanitized when you work.
ALSO, avoid putting it in proximity to bread or bake yeast doughs next to it. Don't ferment beer or sourdough next to it, don't share the cave with other fermented/aged things you are making such as sausage. Your cave should be located out and away from the kitchen (or bathroom).
That blue mold is probably not roqueforti; It is most often saccharomyces cerevisiae - bread /beer yeast that releases freely into the air and is normal to be in a house. While terrible for flavor, it is not dangerous, just a grand annoyance.
As for your fuzzy moulds in the cave - do you have a photo? It could be poil de chat (which is actually desired in many cheeses like Tomme, where yo begin to flatten it a few weeks through and it creates the signature grayish-brownish mold). Usually reducing moisture can help. It can also be Oidium, a fruit yeast-like fungus. Looks like a white powdery cover on grapes and plums but looks totally different when it is attacking cheese. Again, most likely nothing dangerous but an annoyance.
Did you salt the cheese properly?
Also, I am not sure what you are trying to do. Semi-soft or hard cheese in a cave without wax, oil or vacuum seal - will ALWAYS grow these molds. If you want to age it naturally and don't like these molds, then you should inoculate a mold that you like -so that it outgrows the foreign molds (kill them by using all of their nutrients, competition effect). alternatively, you can wash the cheese on a regular basis in brine. It will wipe off some of those mold spores and won't let them grow. It will however also invite B.Linens to develop on your cheese rind ...which isn't a bad thing for many cheeses.