Of course, ignoring all (https://forum.bodybuilding.com/showthread.php?t=140821631&page=1) the plotholes (http://kenlevine.blogspot.com/2015/06/logic-problems-on-gilligans-island.html) that the original series had.

a GREAT Cast could make it work

maybe using comedians like Tim Allen as the professor / Weird Al Yankovich as Gilligan / Fran Dresser & her legs as Ginger, Jane Leeves as Mary Ann, ....

It couldn't be an all white cast now. There would have to be a few persons of color and probably an LGBTQ. They would all have cell phones, although depending on where they were marooned, the phones might not work.