Am I justified in dropping this independent variable? I'm currently doing churn prediction in R and during EDA, I discovered that a variable, say gender, has 1720 males who don't churn, and 280 males who do. Also, it has 864 females who don't churn, and 136 females who do. So roughly 14% of both genders churn and 86% don't. From what I can see, this variable does nothing to explain churn. Am I justified in dropping this variable before I put it into a predictive model? (I have conducted stepwise logistic regression and this variable isn't included in the final call)

I'm sorry if this seems like a very basic or obvious question. I've just started with ML and didn't find a question like this elsewhere. 

EDIT: Gender is highly uncorrelated with other independent variables
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.