Not so safe
There is an argument that decades ago no one knew about allergies and intolerances and we were all perfectly fine, so why all the fuss? Well, just because rolling news didn’t flag up every occasion where someone had a terrible reaction to a bagel doesn’t mean it didn’t happen.
I get that some people are just being a bit LA when they say they can’t eat gluten, but for a large number of others, it’s a substance that causes them physical harm. This is why labeling is important, and why this manufacturer should perhaps look for another line of work before they hurt someone.