This is, surprisingly, more a "Japanese landlords really prefer salarymen" than a "Japanese landlords really anti-prefer foreigners" thing. The second happens, too, but the first preference is more common and harder to talk around.https://twitter.com/james_riney/status/1006387115708514304 …
You'll be able to rent a place; you'll just find it a much, much more annoying process than you're probably used to, and you may need an excessive amount of assistance from socially established folks to make it happen. (Unless you could buy with cash, getting mortgage harder.)