Which is why I thought it the perfect place for a monastic order- monks with a vow of chastity are not expecting to have children anyway. But the fear of that sterility will deter casual (male) visitors.
Not quite. Whatever the "taint" at work on Dawnworld is, it doesn't make visitors or immigrants sterile. Instead, males of Terran-descended species
conceived on Dawnworld are born sterile.
Something on Dawnworld effects males during gestation. That same something doesn't effect males who gestated elsewhere. (That explanation is from Our Absent Friend Hans himself.)
Also, monasticism doesn't necessarily equate celibacy nor physical seclusion. A withdrawal into a "spiritual" life and away from a "worldly" one can occur while living and working among others as the various mendicant orders neatly illustrate.
Mount Athos is just one example among thousands of differing monasteries and Christian monasticism doesn't describe the monastic practices of every current religion let alone those which may exist in the 57th Century. If you avoid the lazy trap of cliche, you've a great chance to create a
"We're not in Kansas anymore..." moment for your players. Let me explain.
Many, many years ago I was refereeing a usual
Traveller campaign. The players had a free trader and were flying around a homemade subsector looking for cargoes and jobs. One of them asked me what the name of the surrounding subsectors were, so I took the map, penciled in a few name on the spur of the moment, and handed it back.
In my hurry, I'd named an adjoining subsector
Stooges.
Traveling there immediately became my players' goal.
By the time they got there, I was ready to play against every assumption and preconception they had. I constantly rubbed their collective noses in the difference between the label of a thing and the thing itself. The subsector wasn't full of short strange men busily hitting each other with pies or destroying plumbing and, while named Moella, the duchess wasn't a violent misanthrope with a soup bowl haircut. The players made all the usual assumptions at first, suffered the consequences, and learned to think rather than presume. They loved it.
You have a similar chance to do the same things to your players. When they here the word "monastery" and "monks", they will blithely assume all sorts of things. It's your job to make all those assumptions false. Your monks should not be wearing coarse brown hassocks, chanting in unison, raising bees, brewing beer, and flagellating themselves because that's exactly what your players will expect.
You can show them a monastery and monks which challenge their assumptions or you can trot out the usual load of cliches and stereotypes. Which way do you think may be more fun? Which way do you think may be more memorable?