Chicago has plenty of grade crossings on rapid transit:
Skokie Swift: https://goo.gl/maps/2PcGgH7NVTv
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Brown line: https://goo.gl/maps/a53AVrYCtnq
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Pink line: https://goo.gl/maps/ZnJFz3L4Yp82
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All are just protected by standard crossing gates. If anything they're actually safer than most other railroad crossings, given that CTA operators see a signal that lets them know the gates are down far enough in advance that they can stop before the crossing, and the shorter stopping distance vs railroad equipment means they are far more likely to be able to stop in time if there's a vehicle blocking the tracks.
Plus there's the countless crossing in third rail territory on Metro-North and LIRR. And other subway systems in the US have private grade crossings, protected with standard railroad crossing gates (e.g. Baltimore Metro at Old Court).
Grade crossings are allowed on rapid transit and/or with third rail. They're not ideal, but they're allowed.