I have a few of these name tags, all of them have this condition. Is this going to have any effect on the weapons or hats I use them on?
It just means you can't use the name tag item itself as part of crafting. It doesn't mean an item you rename can no longer be used in crafting. (I reread that and it sounds as clear as mud, but I hope you get what I am saying.)
It could mean that the named item won't be craftable (which shouldn't be an issue - why would you want to scrap something you've named??). I know that if you craft untradeable items into scrap, then use that scrap to craft a hat, the hat is not tradeable. The non-tradeability passes along with whatever is made from that item. It's possible that craftability passes as well. But that seems like much less of a potential issue than non-tradeability.
It won't transfer to the item. Did you buy the tags from the mann co store? I think almost everything you buy from it comes with that tag and the name tags without it are from random drops.
Ceezyr that might have been the case, I've had the name tags for so long I forgot where they came from