Funny graphic, Mike!
Anyway, I liked the response, above, that explained handling profanity (either enforcing a ban or ignoring it) from the perspective "they asked me to." IOW, we, as umpires, call the game according to the rules and guidelines of the organization putting on the contest.
It is no more "my" field than the game is called according to "my" rules. It is their field, and their rules.
The umbrella ASA organization for greater MN (excludes the cities of Mpls and St Paul) has a casual profanity rule. Rachel, who responded to this thread earlier, calls for that organization, as do I.
So far, I have issued 2 warnings to coaches and one "look" at 18U players for profanity (coaches were the S-bomb in response to missed plays; player was the F-bomb, as a response to a teammate who was giving her some grief about missing a fly ball.) Otherwise, the rule works well, to whatever extent the existance of the rule can be credited with profanity-free games. It's not a big deal to enforce. And Jerry Falwell never comes up.
Understand, I am talking about youth ball. I don't know how well it works for adult ball.