Nope, it doesn't. Being a cleric is still pretty much different from being a wizard -- it's not like the only difference between them is items they are able to attune to.
Like, y'know, reskinning is a thing. Playing a cleric of Mystra as a wizard is a pretty frequent occurrence, and if you are for some stupid reason so opposed to reskinning, then question whether can cleric-not-quite-cleric attune to cleric-only item is pointless. If you aren't, then this question is pretty pointless too -- there's no single reason to not allow said character to attune to the item.