I cannot think of anything specific now (its quite a long time I was dating somebody involved in church activities), but generally, when it interferes with your relationship, plans and goals.
Secular mindset and morality, mixed with beginnings of Christianity. Danger of being unstable or insecure - either leaving the faith or being easily manipulated by some Christians (frequently other women or pastors, various church leaders...), cults, sects. No good examples of working Christian life, therefore various confusion about relationship, marriage, values. Being still influenced a lot by her old lifestyle and habits, for example social apps. Be careful with new believers.
This is individual. Rather define for yourself what you want and then look for it. In any case, realize that dating is just a temporary thing, many Christian women will want it to transform to marriage and family quite soon and will start to be dissatisfied if it stagnates and does not lead to their goals. It may lead to common surprise in men "What happened? Everything is as it was, but she appears to be changing".