People with PhDs in all manner of fields, including English, frequently begin sentences with conjunctions in their academic prose. Mr. Strunk and Mr. White's little treatise could be called outmoded, but more to the point, its usefulness and accuracy were questionable from the outset. A good discussion of Elements of Style's problematic content can be found here.
A somewhat better but less heralded dead-white-guy-talking-about-English-usage-and-grammar book is Theodore Bernstein's Miss Thistlebottom's Hobgoblins.
If this were an actual debate or even a discussion, it would boil down to prescriptivist versus descriptivist takes on grammar. (Strunk and White tried, clumsily, to be prescriptivist. Bernstein was descriptivist.) But the citation of a third-grade teacher's admonishment, backed up by a book whose popularity fails to equal intelligence and accuracy, doesn't rise to the level of debate or discussion. It's mere Internet silliness.