1. "Gentrification" is a loosely defined process which is driven by many complex forces. The word has even seen a substantial drift in meaning over the past 20 years or so, becoming much more general in the process. Gentrification by any definition is fairly impossible to stop, it's more akin to trying to keep a beach from eroding. At a certain point, you have to ask why people don't just fucking move to one of those vacant lots in a dying rust belt town, rather than bitching about the jetty washing away or the Starbucks going up.
2. Anarchists do fuck-all to stop gentrification. In fact, in most cases, their continuous presence in a neighborhood is often like distant thunder on the horizon, a sure sign of an impending storm.
3. Conversely, anarchy, in the layperson's use of the word, has proven to be the only truly effective weapon in fending off gentrification. The new breed of hoodlums all across America who are working hard to keep their neighborhoods trashy and dangerous are like some sort of Taliban insurgency in the ongoing class war.