Yes. Yes they can.

For that matter, I've received written correspondence from people while doing genealogical research with the return address listed as "Mobile, Alabama, Occupied CSA". There are definitely cultural norms that come into play here, but in that particular case - it was from an officer of a chapter of the Sons of Confederate Veterans and contained photocopies of Confederate military records - I was amused by it. I kept the envelope and included it in my own archives.

Now even if it is allowed, suppose this was a Federal government procurement. Will Feds buy something with such flags? Nope. Once that happens, it can be easily demagogued.

Actually, probably. If the item meets the specs and the price, that's what matters.

Just as there is no shortage of federal buildings, and even military installations named after Confederate things.

This HN discussion illustrates how bringing up Confederate themes, you can really tell when someone isn't an American.

Do you know of any counter examples where a company was able to make a successful bid with a product that had good fit, but an inconvenient non-functional addon like that?

The Confederate flag is a bit weird because there's enough of the population that apparently doesn't see it that way, so some stores will even display products that have it. (Personally I find it to be an awful symbol and wouldn't stick around if I saw it displayed).

An example that is more like what you've described is something like a Nazi swastika -- technically you can sell something with a swastika on it (I'm 99.9% sure) but almost no stores would be willing to put it on the shelves, certainly no major chains or whatever.