Am I justified in dropping this independent variable?
If you think it isn't a variable that explains your target variable (churn), you are of course allowed to leave it out - it is in a way then a hand-crafted feature, because you are deliberately telling the model to ignore it (by omitting it).

There are models that would be able to take it into consideration and then decide whether to use it or not, such as component-wise gradient boosting (CWGB) or neural networks. CWGB would simply end up assigning the variable a coefficient of zero if it decides that it doesn't help explain churn rate.

In general, which the percentage split that you gave for males and females, I personally think it could be a valuable feature - even if the model is able to deduce that roughly 14% of all people churn. There might also be correlation between the gender and other features in your dataset that, together, are able to give a stronger signal regarding churn probability.