Re: i feel like this is unprofessional
When people generally refer to a blank shirt, they mean a shirt without any printing on it. Tagless tees or tearaway tagged tees are different than a blank.
If you do not wish to distribute with a tag, be it yours, or someone else's, you will still need to print the same vital information about the shirt in its place. I forget the exact details, but believe it's federal law to include RN#, place of manufacture and wash instructions. If you search for "replace tags" via the search engine on these forums you should be able to find out a bit more information.
As to whether selling with a tag or without is affecting your brand, that depends on what you do and who you're targeting. I personally just leave the tags on, so that people know what they're getting, but most of my printing is either for events, or individuals. I have no real "brand", just my skills and abilities to promote, and if someone comes to me asking for a higher quality tee, then I will inquire further, most of what I do though is just basic t-shirts so I use Gildan 2000's or 5000's. Occasionally I'll order some Alstyle or American Apparel for those wanting a bit higher quality, I've never really gone with Hanes or FotL though. One of these days I'm hoping to get someone really wanting higher echelon and go with Bare Apparel, but my area's fairly despot!