Can't open text file from Finder without extension even though execute flag is not set
When I drop on BBEdit I get messages that say the file cannot be opened because the developer is unknown and “macOS cannot verify that this app is free from malware”. That’s an absurd message for a text file. Any thoughts on fixing this?

You’re right, it is an absurd message, and unfortunately, it can happen with any file that you’ve downloaded from the Internet. It doesn’t have to have the executable ‘bit’ set.
The ‘fix’ for this would have to come from Apple.
However, in the meantime, the only thing you can do is remove the Quarantine flag:
xattr -r -d com.apple.quarantine '/the path/to/The File'
For more information about this bug, see:
Serious flaw in macOS: quarantine can stop you from opening documents – The Eclectic Light Company