I have no problem with local rules. That doesn't mean I just let other things slide, well, because. That's it, just because. This is why I am the ONLY umpire in the world to ever ask for a line-up card, to actually check bats before the game, to require to see the ball off the bench before it gets into the game and the best of all, I was the ONLY umpire to ever make players run the bases on an out of the park HR (before ASA changed the rule).
I told them that was not true. A player asked me if he HAD to run the bases, I said that was up to him if he did not want to. He sat down. When the defense appealed, I rang him up because I didn't tell him NOT to run, just told him he didn't have to if he didn't want to. I'm not his coach.
They protested. They lost.
When asked about umpiring games with amended rules, my standard response is "not a problem, but make sure the 'local' rules are published and you get a copy."
Don't assume anything because players will try to talk an umpire into a "local" rule and all of a sudden, you are getting a call from the city/county/town/league office about a protest because YOU let them do this or that.
There are two leagues in this area with which this is a problem every year. They want "special" rules to allow a 80 yo veteran to pitch, but not bat. Or bat, but have a "courtesy runner" from the plate, or unlimited courtesy runners for the female players they are allowed to use because there are not enough men to have a team. Yep, that would be the Church League and the Firefighter's League.
When the umpire tells them no, s/he is informed by these honest, trustworthy folks that they are special league rules (which there are not). When asked to see a copy, it is unbelievable that there can be six teams in one location and not one of them has a copy of the league rules that do not exist.
How do your local leagues handle exceptions or amendments to the standard rules?