There were studies that didn't do the correlation test thus elimination before being used in maxent model saying that maxent accounts for multicollinearity. But from what I read so far this is an unpopular opinion. There were other studies that also didn't do the collinearity test but they enhanced their model by continuous elimination of variables depending on the jackknife test results. However, most studies do consider testing the correlation and elimination of highly collinear variables before modeling.
On where to do it, yes the SDM toolbox in ArcGIS have an option for that (Double‐click the ‘SDM Tools -> Universal SDM Tools -> Explore Climate Data
-> Remove Highly Correlated Variables ‘.. you can check the tool manual for more details.
The correlation also can be tested in ArcGIS using the PCA (principal component analysis) method where it test variables against each other individually. Also you can do that in R using PCA or VIF (variance inflation factor) test that accounts for multicollinearity between a variable and all other variables at once. Please double check and read to choose what suits your study goal.
Best