Both are State issued licenses how can one be treated differently than the other? Using your theory one state could refuse to recognize a drivers license from other states.
Theoretically they could although Federal interstate highways might be a problem.
But again that isn't the faulty logic with you claim.
The correct comparison would be saying we will honor Drivers License from other State for visitors if they are white (or male, or Christian) but not for blacks (or females, or Jews). You seem to be missing the point that the States are attempting to recognize some but not other certificates based on gender of the individuals involved.
BTW - Every State that I know of - and I don't claim it is all - requires people to get a new Drivers License within some time-frame if they change their residence to that State. Here in Virginia it's 60-days. After that Virginia no longer recognizes the Out-of-State license as permanent authorization to operate a motor vehicle. 60-days after changing residence an individual operating a motor vehicle is breaking Virginia law.
[Disclaimer: There is an exception in the law for active duty military personnel stationed in the State and who maintain a permanent place of residence on file outside the State. Which is why it was legal for me to use my New York license for 4-years after getting stationed here. Once I retired I had to get a VA license.]
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