I believe it is a "red flag" when someone you are dating is interested only in talking religion. In fact, you can broaden this by saying those who only want to have "serious conversations (only what they consider serious subjects). This is not healthy, and it could be a sign of someone not grounded in reality, or narrow and/or close-minded. For two people developing a relationship, it is also possibly a sign that the person is not interested in (or maybe even incapable of) personal relationships. Human relationships demand attention to other persons. Friendship, which is so critical to developing a relationship toward marriage and to a healthy marriage itself, requires that two people always go deeper in knowledge and experience of each other. That is called "intimacy". Marriage provides the ultimate intimacy experience by including sexual expressions that are appropriate only to married couples. Talking only about religion (or only deep subjects) does not explore all the things that make up each person. Religious topics are a "subject". God is THE objective reality of existence and is, therefore, in everything we do, say, experience, etc. He should not be reduced to a "subject".
Because all aspects of life are part of our religious experience, because everything about the human experience includes God, there is not a single aspect of life that should have God excluded. So whether we are interacting with other human beings or with nature, or if we are working, or in school, or eating, God is there. That means we can enjoy life and have relaxing conversations about all kinds of things, not only specifically religious things. Do you see the difference? Sometimes you are praying, but sometimes you are relaxing with lighthearted things. They both (and everything in between) have their place.
Someone who only wants to talk about the teachings of the Church or about things in life that specifically go against Church teaching, with no interest in other aspects of life (which God is very much a part of), usually ends up being a pretty uninteresting, and even boring, person. But it could be worse than that. This type of person can sometimes end up being someone who judges that anything else to talk about is a waste of time or perhaps a sin, and therefore determines that those who desire to talk about or do other things that are not just overtly "religious" are not "Catholic". This is typically tied to a lack of a sense of humor (which is SO important in a person and in marriage).
One of the worst things someone can say to another person is something that specifically indicates another is not being "Catholic". I have had this happen many times in my life. Someone would say, "That is not very Catholic of you." From my experience, very ugly things happen from a person who is bold enough to make a statement like that. So when I hear someone say anything like that, it is a red flag, and I have no dealings with that person (if I can help it). This kind of person judges everything others do or say against their own criteria of what it means to live as a Catholic. This is very dangerous. First and foremost, we are not to JUDGE anyone! No one knows another person's motives, and sin is in the motive! And we are to assume the good in a person, and pray for those who seem to be in error or in sin. But never to judge! If we are capable of doing it without being harmful or making things worse, then we are to (at times) confront someone on what we know as Catholics is not appropriate or is sinful. But we are not to make a way of life out of it.
This kind of person kills a relationship. Not because they are not "Catholic" or a bad "Catholic" or anything like that. It's simply an inappropriate approach to relationships. I guess if two people who only want to talk religion are happy with each other, then God bless them. There is someone for everyone, right? But I'm sure most people will admit that they don't like to talk religion ALL the time (or even most of the time, if we are really honest with ourselves). And it is natural that we don't, and nothing at all to be ashamed of.
God wants us to live a virtuous life by His grace. That means we bring Jesus Christ into everything in our life, including all conversations. It is our example that shows Jesus is with us and that we are Catholic. Therefore, we are careful about what kinds of things we talk about in conversations, or the things we take in through our eyes, etc. This is the way of the Christian. St. Augustine said, "Love God and do what you will." That means that by loving God you will DO God's will in all the various things that make up your life. And it means you are free! Free to talk about lighthearted things, or sports, or movies, or books, or cars, or whatever. But most of all you are free to talk about each other; your loves, your fears, your hobbies, your dreams, your past, your feelings, and yes, even your soul.