The relevant sense of "wake" is: the trail of waves or foam left by a boat as it moves through the water.
The wake is the white stuff, especially the trail immediately behind the boat. (A wake doesn't necessarily have foam, though.)
Your example uses the word "wake" metaphorically. "In the wake of X" is a common metaphor meaning: in the situation resulting from X, especially the end of X or the passing-through of X. The metaphor suggests that X has finished, its end caused a great disruption, and the new, post-X situation is temporary and unsettled but will eventually calm down, just like the jostled water behind the boat. For example, the book Embracing Defeat: Japan in the Wake of World War II is about Japan in the years immediately after World War II, when it was occupied by the United States and adjusting to a new form of government and a new position in the world.
I can't tell for sure, but the metaphor in your example might indeed be a non-native misunderstanding or even a pretentious abuse. The metaphor implies that discriminatory laws against women and children no longer exist, their removal caused great disruption, and now we are in a chaotic period of settling down after that disruption. I don't know if all such laws were recently repealed in Tanzania, resulting in social chaos, but from the author's other tweets, that unlikely event appears not to have happened. So, yes, I think it is probably poorly written.