I mean stands like this:
If there is a little bit of wind or someone pushes your bike when they are trying to park, can the lateral forces damage the wheel?
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I guess it partly depends on the wheel/bicycle. Smaller, sturdier wheels (e.g. 26"/559mm MTBs) should be more resistant. With road bikes I’ve observed that they often lean on the spokes. This is especially bad if you have a low spoke count and therefore a high spoke tension which makes the spokes even less suited for lateral loads. I think it can definitely damage your wheels if it’s especially gusty wind or someone stumbles and runs into your bike really hard. Usually it’s also hard to properly lock your bicycle (since you often can’t put your back wheel into the stand if you have a rear derailleur), leading to the sad event displayed in your second picture. I don’t have disk brakes but I could imagine that you could damage them on some stands as well.
I try to avoid such stands whenever possible.
As a personal anecdote, my dad and I used to transport bicycles on a car trailer using a stand like the one in your first picture. On one occasion we apparently hadn’t tied the bicycles down hard enough and the constant vibration and rubbing completely destroyed the sidewalls of my road tires.