Doesn't Abe still completely support the US presence on Okinawa?
It's a calculated move.
The people of Okinawa want the US bases gone.
Abe (as well as the people who own the land the US army rents for its expatriates - at triple the market price) wants them to stay.
The Okinawan public opinion has made a clear choice, and expressed it multiple times in a row through vote.
The current governor, Takeshi Onaga (a dissident from Abe's party, the LDP), was elected solely on the promise he'd get the bases moved out of Okinawa.
His predecessor, Hirokazu Nakaima, who had full support of the LDP, was elected on the exact same promise.
During his stay as governor, he managed to pretend he was actually trying to do something about the issue, because the opposing party (DPJ) came to briefly rule the country (2009-2012). But when the LDP came back in full force with Abe at its head (2012), he backpedaled as a motherfucker until the end of his mandate (2014), and came to an agreement with Abe, deciding that one base, Futenma, would be moved from its current location in the comparatively populous city of Ginowan in order to be fused with Camp Schwab in Henoko, in the North of the island.
The people of Okinawa felt betrayed; despite the presence of Camp Schwab, Henoko remains a fairly beautiful coastal site, and the people naturally came to say that if the bases were to stay in Okinawa, there was no point in moving them there.
So Nakaima was quickly ousted in the following election.
But Abe insists. A deal is a deal (and rumor has it his friends have already secured the land in Henoko) so he wants the move.
Onaga is trying his best to strong-arm him, in order to reverse the Henoko agreement and put back on the table the idea of a move outside the prefecture. But in order to succeed, he'd need the understanding of the rest of the Japanese population.
To undermine his efforts, Abe has methodically jumped on each and every single opportunity to justify the move to Henoko. His core argument is: "the farther the US army is from the general population, the smaller the risks of incidents".
So whenever an incident occurs, he does a public stunt. His endgame is not to try and convince the Okinawan population. At this point, that's a lost cause. All he wants is to keep his voters in line in the rest of the country.
To the people who don't live in Okinawa and don't give much of a fuck about it, his rationale does appear to make sense: every time a crime is committed by an American in Okinawa- be it far from Futenma, like the rape incident that occurred in Naha a few months ago- Abe rushing to the mic and yelling "see? I told you, the priority is to move move those bases away from the population!" makes him appear like a man who cares. For free. And it makes the people of Okinawa look like fools for wanting more than the move to Henoko he offers.