What is the opinion about Catholics and non-Christians in a relationship?
My short answer: Ideally, spouses should be the same faith, whether that shared faith be Catholicism, Orthodox Judaism, Buddhism, etc. Couples who have one person convert after the marriage are in a class by themselves, and the converting spouse should be supported and encouraged.
My long answer: With regards to non-marital, but romantic relationships (courtship/dating), it depends. If one person wants to convert for the sake of their soul (and not the significant other), I see no reason why the relationship shouldn’t progress toward marriage. If both are strong in their respective faiths, I believe that a lot of hardship is almost inevitable, and in most cases, marriage would not be wise. Sharing spirituality and raising children in one faith are very important to me.
My experience (which explains my opinions

): I was unbaptized when my husband (a cradle Catholic) and I met at 15 years old. We started dating at 17, and I did not become Catholic until I was nearly 20. He proposed 7 months after my baptism, and we married 2 years later.
One of our first dates was Mass. I asked him to take me, and he said that his family didn’t really go that often. He told me that because I was so interested in going, and I was looking for a man strong in faith with whom to have a family, he started going every week.
At the time, I would not date someone who didn’t take his faith seriously, because I was searching for the Truth and I wasn’t going to get involved with anyone who was mediocre in his faith. I grew up in a “choose your own faith” family, and did not want to repeat that experience with my children. I latched on to Catholicism (my dad is Catholic, so I had a bit of a cultural Catholic upbringing) because of its history and pro-life stance.