Will using this kind of parking rack damage the wheel?
These stands don't hold the bike very well because if the friction grip fails, the bike can roll/move backwards and then fall over as the steering turns.

So, consider backing your bike into one instead of going in frontwards.  Downside as ChrisH says is that your lock needs to go from the rack all the way to the front wheel, or use two locks.

Also check the stand is bolted to the ground and that there are no cuts through the metal.