Ihr dürft es nicht sehen - you may not/ are not allowed to see it Ihr dürft das nicht sehen - you may not/are not allowed to see that
The differences between can and may are quite nuanced. Can is frequently used for permission in modern English, although everyone knows it is considered "wrong" to do so. And may is often used to indicate ability to to something, not just permission. "You may not see the ocean yet, children. It's still a bit far away". I suppose you could consider this ellipsis for "You may not be able to see the ocean", with the missing "be able" providing the "ability to do" part of the equation. But "may" does not imply just permission. It implies possibility, and I think this is what we have here - a half-way house between permission and ability. The same applies in the conditional uses. "Sorry John, I could do it but I don't think I should". Is he implying with could that he may, or that he can, or that it is possible? I don't know. Take your pick.
You CAN'T translate "may not" to "nicht dürfen"! "Nicht dürfen" ist much stronger than "may not"; a propper translation would be "nicht dürfen" = "must not".
dedicated user I agree completely with you. correct translation here would be you must not see it... you may not see it.... in German would be... du kannst es vielleicht nicht sehen.... nowhere near ... you are not allowed to see it.... you may not see it... if you emphasise the negative.... that you are not allowed to see it... you would translate it into... Es ist besser wenn du es nicht siehst.
"You may not see it" and "You can't see it" have different meanings." The first involves permission. For example I am not allowing you to see my passport photo. The second involves ability. For example, we are still too far away so you cannot see it yet but soon you will see the ocean.
Unless you're conversing with people that don't mean it that way. "You may not see it" is often used to mean "You might not see it." At least in the US this is pretty common. Also people often use "can" for permission. Children are often corrected for such use, but it is still somewhat common usage.