Paolo Ruffini's work on the impossibility of solving the quintic by radicals did meet a strong passive resistance. Around 1800 he proved the theorem up to a minor gap, that himself or somebody else could have fixed soon, had his book met the attention that deserved. But times were not ready for a such a revolutionary idea as proving the impossibility; 20-30 years later this idea had slowly spread and become more natural, and Abel and Galois got more lucky (so to speak).
This is in my opinion a major example of a particular theorem that was met with resistance before being accepted, and in fact it also shows that resistance is not necessarily associated with controversials, but sometimes even with indifference (which may be even worse).
A short and well written account of the story is in J.J.O'Connor and E.F.Robertson's article for the History of Mathematics archive: http://www-history.mcs.st-and.ac.uk/Biographies/Ruffini.html)