No. Double negative rules apply to modifying a negative, but in this context the first DNI should not be considered a negative but a noun in its own right.
First DNI: Men, do not interact with me.
Second DNI: Do not interact with me, misandrists.
The second is not literally the same thing as “men, interact with me” but it can be assumed to mean “I don’t have a problem with men interacting with me.” It is still is not a request for the interaction itself which is what double negative rules would imply.
Tl;Dr double negative rules in English simply aren’t the same as they are in Latin which is why it’s a fake rule, even beyond the usage for emphasis in casual speech.
I mean, Caesar more or less hit it and quit it so it’s got some downsides