Certain chords were considered heretical in the early years of church music. Even the BASIC TRIAD chord was considered heretical at some early point - open 5ths were OK, the 3rds were considered to be the "problem".
Just consider: the most common source for a Mass setting during this period was to use a popular song as a cantus firmus or recurrent theme - one example is Dufay's Mass 'l'Homme armé', based on a popular ditty that probably originated with the Crusades. If secular music was so heretical, what were all the major composers doing using it to set Masses?
It is true that some intervals were considered "imperfect" but that has nothing to do with the Church and everything to do with the ancient Greek theories of music.
It's difficult for us to understand what the problem was now, because we all are used to the adjusted or tempered Western scale -- based on the piano scale, which is not a true even division of the octave. The medievals inherited the "Pythagorean tuning", which WAS an equal division, so you have to have one place in the scale where the interval sounds cranky. Especially if you're playing in different keys -- if you start with a pretty good tuning in in C Major, you're going to be WAY out by the time you get around to, say, A flat major.
What you are thinking of as a "third" was actually an augmented fourth in modern terms -- that's why it was considered the "devil's interval" - it sounded like the devil (still does). That term, by the way, didn't show up until much later, the medievals called it a "wolf interval" because it howled like a wolf.