Will a bike stand that holds one wheel damage my bike? 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.