Can I simply remove one of two predictor variables that are highly non-linearly correlated? I understood why we should avoid having linearly correlated variables in our model as asked in this question remove one of two linearly correlated variables.\
But should we do the same when we face non-linear relationship ?
(In the case i would want to do a logistic regression logistic)

 A: So you have a logistic regression with one observed binary response and two numerical predictors, non-linearly correlated as shown in the plots?
The reason for (maybe) leave out one predictor in the case of high linear correlation, is to avoid numerical instability. With the non-linear correlation shown in your plots, there will be no such numerical instability, so that reason do not apply.
Edit I answered the question above, tentatively, assuming it is an isolated question with a constructed example. For a real example, there could be more predictors, not known or shown here, and that might change the conclusion, as alluded to by @whuber in a comment below.
A: Assume a case where we have definite understanding of the driving variable in a process.
However, we are forced to employ a proxy variable, which by definition is not directly relevant, but assist in place of an otherwise, say, not timely observable or measurable key variable.
Now, in this context, regardless of the functional form of the imprecise proxy variable, is it conceivable that one could have a combination of two proxy variables that nevertheless improves the estimation of the known driving variable.
So my answer is a very tentative yes. My guiding recommendation, however, is certainly not always and best performed where one can quantify the precision of the improvement from employing multiple proxy variables if any.
Clearly, working with non-linear models, this even becomes more difficult, and perhaps less probabilistically accurate, even in quantifiable situations.
