Should I join an NIT which doesn’t allow MSc students to do their final year project outside?

If NIT doesn’t allow MSc project outside, then this shouldn’t be a reason to reject NIT. You can always work unofficially with any professor outside. Nobody will deny you that. And NIT professors are not that bad, you can do your official MSc project with them. But you are free to work and take guidance from any outside professor. You can utilise your summer, dussera and winter vacation to visit other institutes.