The convergence is massive and even faster than in the 90s. Languages die nearly daily (a language dies when its last speaker dies) and with them their culture, and people consume the same media and news all of the world. I'm not going to dig up some links on the net, you can do that yourself, but these are measurable phenomena.

You're thinking in short, next twenty years or so. A resurgence of nationalism is a response to globalization, but unless we give up our ways of living entirely (no capitalism, no markets, no growth) these movements will have practically no effect. Mass media alone ensure that, let alone the nature of global trading and social mobility. Think about the next two hundred years and there is no way culture on earth will not be vastly homogeneous. Whether that's good or bad I will leave open, my personal view is that all massive shifts in human development are accompanied by positive and negative effects.