Does tightening a QR skewer in different ways affect wheel alignment?
It is possible that when you put in your wheel into the drops you are not seating it all the way before tightening the QR.
This can lead to the wheel being slightly off angle that would lead to rubbing.
The fix for this is some people will install wheels when the bike is on the ground to prevent this or alternatively you need to apply pressure into the drops as you close the quick release when the bike is firmly in a stand.
I tend to use the second approach as often when I remove the wheel the bike is in a work stand. I have found that once I reach the normal tension prior to closing the QR usually snug and such that when I close the QR it leaves an impression in my palm, that any alignment issues usually have to do with not getting the wheel all the way into the drops.
Another possibility, which I do not think is the case is your wheels could be out of true and that is fixed by adjusting spoke tension.