This is a tricky thing. Ostensibly, you buy a business to make money, earn a return on investment, generate cash flow etc.
The folks who buy newspapers are swimming against the tide anyway, as newspapers are having a hard time keeping eyeballs right now. To buy a newspaper that is prospering in a pro gun environment, promoting pro gun views maybe, and turn it into the opposite is very courageous. To buy one that has been losing revenue, customers and money in hopes of turning it around is even more so. As Warren Buffett put it, "When a management with a reputation for brilliance tackles a business with a reputation for bad economics, it is the reputation of the business that remains intact."
Nobody HAS to read a newspaper, or advertize in one. There are work-arounds, unless you are the local supermarket running full page ads for specials every week, etc.
Customers ultimately determine a business' policies.
People who are pro gun will eventually get tired of an anti-newspaper and not subscribe anymore, if the anti slant becomes prominent. Or, they get lots of practice writing letters to the editor, pointing out the absurdities in the editorial slant. It might be the start of a whole new career for someone.
If you try to offend nobody, you will eventually offend everybody.
And, if you get too crazy, some busybody might be tempted to start up another newspaper and attract all your eyeballs.