Is being a student in one of the exact-science fields at an educational institution considered secular (in terms of how it conducts itself and the atmosphere there), to a degree that could negatively affect a particular person’s religious conduct—something not recommended, even to the point of giving up studying at that institution?

Why does it matter whether we’re talking about the exact sciences or some other field? The question is whether it is proper or worthwhile to study at a secular institution.
If you have an equivalent option at a religious institution, that’s preferable. If not, you need to weigh how important this is to you, what the difference in level is between the two institutions, and how much spiritual harm it might cause you. There’s no general answer that is right for everyone.