Generally speaking, the career opportunities after graduation are not significantly different between Catholic college graduates and non-Catholic college graduates. Typically, whether the university is Catholic does not have much bearing on career opportunities for the students. There are some exceptions, of course.
For example, many Catholic colleges have a close-knit alumni network, which does increase the chances for upcoming graduates and recent graduates to find work opportunities. Using the Catholic college's career center or even just connecting directly with alumni is a great way to build network connections and get a foot in the door. It is not uncommon for alumni to hire graduates from their alma mater, especially if the alumni network is tight.
Sometimes the employer's feelings toward the Catholic religion (positive or negative) can play a part in the hiring process. Employers who share the Catholic faith or a positive relationship with the religion may be more likely to hire someone from a Catholic college than others. On the other hand, those with a negative outlook on religion or, more specifically, Catholicism may be less inclined to hire someone from a Catholic college. However, this is generally not an issue, nor is it expected.
A far more relevant factor when it comes to career opportunities are the prestige of the college and the experience of the applicant. Some Catholic colleges are renowned for their academic excellence and graduate success. In these cases, it isn't so much that the “Catholic” part of the education increases employment opportunities as it is that the excellence of the college and its good reputation do.
So, typically the career opportunities after graduation are relatively similar between Catholic colleges and non-Catholic colleges. An employer's specific preferences will play a part in any case, as will the perceived prestige of the college, but usually the fact that a college is “Catholic” does not factor into the employment decisions very much.