I doubt a Mando Jedi would give his weapon so easy. But this just goes more to show how Disney doesn't focus on the stuff they should. A Mandalorian jedi from The Old Republic is ripe for stories.
True, despite that I feel there's way too much focus on Mandos, but give the people what they want.
I guess giving up his weapon would have to boil down to whether or not he respected the Order enough to obey their wishes versus the Mando Way. I would love to know how then Shae even knows about the the saber, and whether or not she became part of a more zealous sect of Mando's (like the Children of the Watch) that demand that all Mandalorian artifacts return home. I mean there is a lot of interesting history that could be being explored instead of the Rat's boring stories. Like how the Taung of Coruscant were the original Mandalorians. Or like the story of Cassus Fett. You could actually do a series that focused on different major chapters of Mando history each season, even go through various iterations of Mand'alor. I'd watch that series.
