Yes, it can still matter, and feeling this way is not a contradiction — even though a lot of people are told it is.
The accusation usually arrives as a question: if you do not keep any of it, why does it matter who you marry? It sounds like a reasonable point. It rests on an assumption that does not hold: that Jewish identity is primarily a set of religious beliefs, so that if you do not hold the beliefs you have no stake in the rest.
For a great many Jews that is simply not how identity works.
What the feeling usually is
When people manage to articulate it, it tends to come out as some mix of the following.
Continuity. A sense of being one link in something long, and not wanting to be the point where it stops. This is frequently the strongest current and the hardest to admit, because it sounds grandiose said out loud.
Recognition. The shorthand. Not having to explain what a shiva is, or why you are strange in September, or what your grandmother meant. People underrate how much energy this saves over decades.
Family. Not wanting your parents to be quietly sad for the rest of their lives. Worth naming as its own thing, and worth distinguishing from what you want.
Children. The most common trigger. People who genuinely did not care at twenty-five often find this arrives around the time children become real rather than theoretical.
History. A protectiveness that is hard to justify in argument and does not need to be. Given the last century, it is not irrational.
None of those require belief in anything. They are about belonging, not doctrine.
Culture, custom, and law are three different things
It helps to keep these separate, because people arguing about this conflate them constantly.
That traditional halachah does not recognise a marriage between a Jew and a non-Jew is a legal position within Jewish law. Whether you personally feel bound by halachah is a separate question, and for many Jews the answer is no.
That you feel a pull toward marrying Jewish is a matter of identity and belonging. It is not a religious claim, and you do not need to justify it in religious terms.
Those two can point the same direction without being the same thing. You are allowed to hold the second without the first. Plenty of people do.
The uncomfortable follow-up
Here is the question that usually goes unasked: if being Jewish matters enough to determine who you marry, does it matter enough to show up anywhere else in your life?
That is not a rebuke. Lots of people conclude, honestly, that it does not — that this is about lineage and belonging rather than practice, and they are at peace with that. That is a coherent position.
But a fair number of people, asked directly, find the answer is no, and that they would like it to be yes. That is worth knowing before you marry, because it changes what you should be looking for. Someone whose Jewish life is purely cultural is a different match than someone who wants Friday nights to mean something — and both of them may describe themselves, accurately, as “Jewish but not religious”.
Where this goes wrong in dating
The common failure is stating the requirement and stopping there. “They have to be Jewish” is a filter, not a description, and it can leave you matched with someone who meets the criterion and wants an entirely different life.
Two people who both say “Jewish, not religious” can mean: Shabbat dinner most weeks with family, versus nothing Jewish except an opinion about Israel. Both are legitimate. They do not make the same home.
The useful move is to describe the home rather than the label. That is what the Jewish Home Vision tool is for — it asks about twelve areas of Jewish life, separately, and gives you back a description rather than a denomination. It is also the single best preparation for the conversation with someone you are seeing.
Related reading: What if I feel Jewish but I am not religious? and Can two Jews with very different levels of observance build a marriage?