While it's perfectly understandable why you've responded to the changing environment of startups, the lack of holding a position for long enough is a career-limiting move.
It sucks, but the world isn't fair.
is it though? I see people hoping all the time. Sure you're bound to run into a situation where somebody will view that as a negative but the only way you can switch jobs every 2 years is if somebody hired you. Which means that by definition, there will be companies that don't care.
I guess in a tightening market you'll have more candidates without job hopping so you can use it as a criteria but if your company has legitimate vertical movement there's probably less to worry about. Of course though if you company staffs its ranks pretty entirely by hiring outside as opposed to internal promotion then you should expect to replace the role in a couple of years.