I’m a photographer regardless of the platform or the device I’m using period. Photographs on Instagram my not necessarily be your portfolio but treating it as such gives you the incentive to share only photos that you’re proud of. Is this way of thinking for everyone? Probably not because not everyone is a photographer and that’s ok.
My 2c, the act of taking a photograph makes you a photographer. Taking it one step further, you could sub-categorise photographers into professional (those who make the bulk of their income from photography), and amateur (the rest of us).