I've boarded at a few places with stallions and never had any bother with them. But it depends on the horse.
One was an ex-Arab breeding barn and by the time I was there, the stallion was in 20s. Never a more gentlemanly horse have you met. Just a lovely temperament.
At another barn where I worked for a little while, which was mostly full of the trainer's German imports and a few boarders (most of whom worked there), there was an American Warmblood stallion owned by a boarder. That horse was far better behaved than the trainer's fancy Hanoverian geldings. If you got to work with him and saved one badly mannered Hanoverian that day, you were having a good day.
Then at another barn I was at, the owner let a pal of hers attempt to keep her Highland stallion there as an experiment, to see how he got on at a busy yard with lots of people, mares, and geldings about. The experiment didn't last very long, as the horse started getting a little nutty every time a mare went past his stall or field, and the girls who worked at the barn were having a harder and harder time handling him.
This horse had spent his life on his owner's farm, with his own little herd of mares, and had never been away or surrounded by horses which weren't "his" 'till she brought him to the stable in Edinburgh. The two horses mentioned above had spent their lives at stables where lots was going on which didn't involve them or breeding.