As Al said, no way to avoid the cheeses "sharing" with each other -- but at the same time, this is a problem that can be managed. Options:
1) Wash / scrub / scrape your cheeses -- whenever a spot appears, wipe it off with a paper towel moistened with white wine or with vinegar; vinegar+salt makes an effective scrubbing compound if you need more aggressive cleaning. Sometimes if the mold is just barely on the surface, I have lightly scraped it off without compromising the rind underneath. This option can be combined with either/both of the next two options ...
2) Discourage the mold via lower humidity: if you are not actively trying to encourage mold, e.g. on a tomme or a wrapped cheddar, you may be able to get by with a lower-humidity environment. You can't go too low without running the risk of rinds cracking, but I find I can keep my "cave" at around 70-75% RH, low enough to provide less encouragement to molds, though it doesn't totally prevent them, but still enough that the cheeses I make do not crack as they dry. For cheeses that do need more humidity, e.g. bloomies or blues, I put into a ripening box to get localized high humidity. For any cheeses that you will age for more than a few weeks, not in a ripening box, you will almost certainly want to combine this with either/both the previous and the next options ...
3) Wax and/or vac-bag your cheeses -- as long as they are sealed up from oxygen, molds won't grow. In my not-too-extensive experience, wax can develop a pinhole, allowing a spot of blue or other molds; this is much less likely with vac-bags ... but I have had some mold get into the vac bags, suggesting a fault in the seal. I generally try to let my cheeses dry in the cave for at least a couple of weeks, using #1 and/or #2 to keep mold under control, and then, with any mold scrubbed/scraped/wiped off, put them in vac-bags for the remainder of their aging. However, with something like a Caerphilly or Lancashire, I often let them age out (3 or 6 weeks, respectively) without bagging; after the first couple of weeks, the rind is dry enough that very little mold continues to form.
4) Outcompete the mold -- I suspect this is largely the point of encouraging B. Linens to develop on an alpine style by washing with a weak brine/wine solution, and then, once it is well established, letting it dry so the B. Linens does not go further. In addition to alpines, I've done this with Lancashire or Caerphilly; this adds a layer of complexity to the flavor which I quite like ... along with a bit of smell which my wife detests.
It seems, once the B. Linens is going, that very little blue mold will appear, though if it does, just wipe/scrub as in #1. I have also vac-bagged a cheese like this at the point where I don't want it to get any drier.
5) Outcompete the mold by celebrating other molds -- a variation of #4, and relevant to a tomme style or bandaged cheddar. For these cheeses, you encourage a variety of molds to develop on the outside; they will add complexity of flavor, but also they will reach a point of saturation on the rind, without really invading the paste, assuming the rind is well developed. Full disclosure: I've never attempted this type of approach, but many others here have, with pictures attached to show the results!
