Ok, I see.
Usually, the dry throat is a sign that you are mouth breathing, but that is not always necessarily the case.
My question is does the tape fully close your mouth, or is there some areas of your lips without tape?
Because as humans we tend to find ways to make our lifes easier, and subconciously find shortcuts. So it could be that you are actually still opening your mouth in the areas where there is no tape. I would know, because I had that same issue.
If that is not the case, then it is nothing mewing related, if anything mewing can increase the secretion of saliva, and should not make you mouth dryer. If thats the case there is nothing to worry about.