The Catholic Church has not in my lifetime frowned on baptizing the children of single parents just because the parent was unmarried, or had gotten pregnant out of wedlock. This may have been an issue prior to Vatican II. In those days, often the couple would marry, or the girl would put the baby up for adoption, or the grandparents would pretend the baby was a late child of theirs, in order to avoid scandal.
By the 80s, any stigma attached to unwed pregnancy had largely disappeared. As I said, girls in my Catholic high school who got pregnant not only finished school but would be bringing their baby to school events, openly.
A priest will sometimes refuse to baptize the child if he feels the parent will not make a sincere effort to raise the child in the Church. He could get that impression from things the parent says or does or from the parent’s lifestyle or habits or lack of religious practice. Occasionally, individual priests might also make a wrong judgment based on their own biases or opinions, that doesn’t comport with the teaching of the Church.