This sounds like the Darksword series by Margaret Weis and Tracy Hickman. The first book Forging the Darksword was published in 1988 so that fits the time you remember reading it.
The protagonist, Joram, is born without any magic, and the book follows his quest for the Darksword.
The Catalysts are exactly as you describe. I was looking to see if there is a passage in the book that describes the Catalysts, but there isn't really. We are shown them rather than being told about them.
The Field Magi are described as:
The Mystery of Earth is the most common of the Mysteries, accounting for the majority of people residing in Thimhallan. Among these are the lowest caste in the land—the Field Magi, those who tend the crops.
Re the illegal way to have a child, marriages are strictly controlled to ensure magic is maximised:
Marriages are always arranged in Thimhallan and are, in general, controlled by the catalysts. This is due to the gift of the Vision. The only remnant left of the once flourishing art of divination, the Vision allows the catalysts to foresee if a union will produce issue and will therefore be a wise match. If no issue is foreseen as forthcoming, the marriage is forbidden.
In chapter 9 Joran meets Anja who who tells him:
“I was the daughter of one of the noblest houses in Merilon,” she repeated, combing out Joram’s hair. “Your father was House Catalyst. He, too, came of noble blood. My father refused to have a catalyst living with us like Father Tolban—little better than a Field Magus himself. I was sixteen, Your father was just turned thirty.”
“We went to the catalysts for permission to marry. They performed a Vision. The answer was no. They said we would not produce living issue!
We were desperate. Then, one night, he told me that he knew of a way—an ancient, forbidden way—that we could use to produce a child.”
“He described the ancient way to me,” she said softly. “I was sickened. It was … bestial. How could I do it? How could he? Yet, how could we not? For if he left me, I would die. We sneaked off …”
Anja’a voice dropped to where Joram could just barely hear her.
“I remember little of the night you were conceived. He … your father … gave me a drink made of some bright red flower …. It seems to me that my soul left my body, leaving the body for him to do with it as he would. As if in a dream … I remember his hands touching me … I remember an awful, searing pain. I remember … a sweetness …
The Darksword series has been asked about many times before. It might be interesting to look at some of the previous questions to see if they include more details you remember.