According to this morning's After Deadline post, that's what Philip B. Corbett at the New York Times calls "rules that aren't", following the lead of Theodore M. Bernstein:
Another pet peeve of some After Deadline commenters is the use of “but” or “and” to begin a sentence — as in the third sentence of the previous section. Obviously, I don’t share their aversion.
It shouldn’t be overdone, but using coordinating conjunctions this way can provide a handy and very efficient transition. “But” is certainly preferable in many cases to the stilted “however,” and “and” is simpler than “in addition” or similar phrases.
I’d put this objection in the category of “Miss Thistlebottom’s hobgoblins.” That’s how the former Times language guru Theodore M. Bernstein described overly fastidious rules and usage myths a grade-school English teacher might invoke to keep her pupils’ prose on a very narrow path. (Familiar examples include “Never split an infinitive” and “Never end a sentence with a preposition.”)
Mr. Corbett is being polite to his commenters, I think, by calling these strictures "overly fastidious" (as opposed, say, to "preposterous fabrications").
Arnold Zwicky has suggested the term "Zombie Rule" for things like this — see "When zombie rules attack", 8/26/2008, and "However, …", 11/1/2006, and "Five more thoughts on the that rule", 5/22/2005. In a comment, Language Hat once mentioned "Aloysius Thistlebottom and his fellow half-dozen members of the Preserve English the Way it Was in Queen Victoria's Time (But Not Much Further Back Because Then It Gets to Be Too Much Trouble) Society", so apparently the Thistlebottom family has more than one member in this line of work.
Perhaps Miss Fidditch, who would "rather parse than eat", is a relative. (She's the patron saint of computational linguistics, or at least she should be. Don Hindle named a parser after her, about 20 years ago, but she's been neglected in recent years. )