I don't think I'd worry much about it. Presidents day is pretty much a "bank holiday" only. No mail too... You won't be offending any race or veterans. Unless you mow for any ex-presidents, lol. I'd go ahead and run my route, if you get to a house and they are all home and in the yard, skip'em till the next day.
Your monday customers surely are used to you being there on holidays, there's a lot of monday holidays thru the year...
while i won't be mowing because everything is under snow and dormant i think your point is more about working on a holiday correct?
i'm gonna give my 2 cents about working on holidays.
the only holidays i DON'T work on are thanksgiving, christmas and any holiday that would fall on a sunday. otherwise i'm out doing something somewhere. i'd like to put in full days on those holidays but i know the clients that are off and spending time with family aren't gonna wanna hear all that noise from the equipment so i usually check to see which one's care and which one's don't. obiviously the one's that don't are where i'm at that day.