I have a similar bike stand to this at home:
I'm happy putting my wife's and my commuter in it but worried that it will damage the wheels of my XC bike if left in there for long periods. Can wheels get damaged if there is prolonged pressure on a group of spokes?
I'm guessing from the way you worded this "pressure on a group of spokes" that there is in fact pressure on spokes when you put your CX bike in this rack. Assuming that, then yes, this rack can cause damage to the wheel. The most likely issue you would have is that the wheel would go out of true and you'd have to true it up. My bigger concern would be your CX bike getting bumped when another bike is being put in/taken out. With the spokes already hitting, you could now bend one or more spokes and the truing process just got a lot harder.
That said, I've racked my bikes in racks where there was a bit of pressure on the spokes for short periods without issue. Long term, you may want to find a better spot for the CX.
Directly answering your question though, a stand that only holds one wheel can do so without damaging the bike...it just needs to be wide enough.
I'd be concerned if you you were hooking your trusty XC bike up to a public rack that looked like that, not only would it be nearly impossible to secure your frame to it but I'd fear someone would come along and indeed damage something, even unintentionally while wrestling their bike free from the same rack.
But at home? It depends on how long you plan to leave it there or whether or not it's actually leaning on just a spoke or two. One night at a time? Probably not worth worrying about. Leaving it there for an entire season or two? I probably would skip the risk by leaning it against a wall in a safe spot.
In my experience, these kind of racks do get the wheel out of true, especially if a) there is too much clearance between the wheel and the supports b) your frame is heavy. I would avoid using them particularly in outside windy environments.
