Culture is as useless as an authoritative basis for ethics as is religion (plus, I would tend to consider religion a form of culture). That is to say: Yes, my ethics certainly are influenced by culture (and probably even by religion, even though I am not religious, simply due to religion's influence on culture in general), but if someone were to challenge the ethics of some action of mine, "because my culture says so!" is as bad a defense of my position as "because my holy book says so!"

Culture, if anything, is a shortcut for learning about ethical behaviour from others, just as school is a shortcut for learning about, I dunno, the mechanics of rigid bodies from others, but whether what we learn from either of those sources is (tentatively) correct can be determined only by observation of reality/by experiment.

If you think that ethics is something that needs to somehow be provided by someone rather than a property of reality that is to be discovered, that is already a religious presupposition. Sensible ethics are utilitarian/consequentialist: You look at what causes harm and what avoids harm to build an understanding of ethical behaviour. It's not much different from what we do to figure out what is healthy: There is no source of health rules with a book that is not to be questioned, but you look at what causes harm and what avoids harm, and that then is what we label as "healthy" or "unhealthy".