This can get a little confusing, but try to hang with me here. First of all, here is the passage in question:
28 We know that in everything God works for good with those who love him, who are called according to his purpose. 29 For those whom he foreknew he also predestined to be conformed to the image of his Son, in order that he might be the first-born among many brethren. 30 And those whom he predestined he also called; and those whom he called he also justified; and those whom he justified he also glorified.You might be surprised to learn that Catholics believe in predestination, we just don't understand it the same way that Protestants (particularly Calvinists) understand it.
Now, what is predestination? It involves a lot of things. Catholics believe that God has a plan for the world and everything in it. This plan was written from the very beginning. We also believe that this plan mysteriously incorporates the free-will actions of men. As the Catechism says, "To God, all moments of time are present in their immediacy. When therefore he establishes his eternal plan of 'predestination', he includes in it each person's free response to his grace" (no. 600). God alone initiates salvation (in other words, the first initiative is always His), and this salvation is extended to all men. It is possible for all men to be saved. If some of them aren't, it is not because God has decreed that they be sent to Hell, but because they have destroyed the divine life within their souls and have persisted in this state. "God predestines no one to go to hell" (CCC, no. 1037).
These are the basic parameters of the Catholic understanding of predestination. Within these parameters, there is room for debate concerning how all of this works itself out.
Regarding, Rom 8:28-30, we see that some are selected for divine adoption by an eternal decree of God. That’s basically what predestination is. These elect were chosen because, in His foreknowledge, God saw that these souls would respond to His grace and persevere in it. “For those whom he foreknew he also predestined” (vs. 29). When they respond to this grace they are added to the family of God, so that Jesus becomes “the first-born among many brethren” (vs. 29). They are justified, and ultimately glorified (vs. 30).
Essentially, this passage is about the plan of God for our salvation and the power of God’s grace to achieve it. Nothing here is contrary to Catholic teaching.