DaasYachid: This is a problem, but not a Jewish problem. The anti-vaccine movement is broader throughout society, and is not specificially a “Jewish” issue. No one perceives this as a “Jewish” matter, except perhaps us. No one is claiming that there is an anti-vaccine Jewish perspective, and Jews are probably less likely than goyim to be avoiding vaccines.
Of course it is a matter that affects us, and of course it has historically been the responsibility of the rabbanim to provide leadership. But it isn’t really a matter of “hillul ha-Shem” any more than people catching any other disease is a matter of “hillul ha-Shem”.