Please see a related answer here.

Jews are both an ethnic group and a religion. They are, in fact, an ethnoreligious group. Jews are related genetically, and share a common identity. That identity has religion as a primary component, at least historically. But, Jewish identity includes things that religious identity doesn't. People can identify as Jewish without being religious at all. Nowadays people also identify as "half-Jewish", which doesn't make sense if being Jewish is all about religion. Besides, Judaism is hereditary, not based on actual personal belief, and endogamy is one of Judaism's main practices (or was, historically).

Honestly, that combination makes a lot of sense. Religious identity and practices can form an important part of cultural identity. There's no particular reason to separate out practices that are originally for non-religious reasons from ones that are religious for the purposes of identity. The reason for lots of Jewish cuisine has to do with religious dietary restrictions, but it's more than that--many Jews eat Jewish foods even if they don't care about dietary restrictions. The same could be said for a lot of Jewish religious practices--mourning customs, marriage customs, naming customs, etc are all religious in nature, but are part of a cultural background Jews share, in that it's just "how things are done", regardless of the origin of the custom (those specific things are broadly shared among Jewish groups that have different cultures in other ways). A lot of this has to do with Judaism having a religious practice for everything, so practices of religious origins may not be explicitly religious and, if practitioners are doing them irrespective of the religious nature of the customs, it wouldn't make much sense to describe them in exclusively religious terms.

tl;dr Jews form both an ethnic/cultural group and a religious group. The ethnic and cultural identity owes a lot to the common religion, but just because a practice is religious doesn't make it not part of a culture. Jews today may identify as Jewish in either sense (or both).