If the NYT had any character at all, employees who felt this way about the flag and the USA would be fired on the spot.
Their freedom of speech would not be impaired in any way as they would still be free to write a letter to the editor.
But they would no longer be employees using their position with the company to damage America.
Gay is known for her memorable mistake on MSNBC last year when she believed billionaire Michael Bloomberg could have provided $1 million to every American with the $500 million he spent on his failed presidential campaign. The actual amount was less than $2 per person.