According to Jürgen Todenhöfer who spent 10 days in the “Islamic State” last year, Israel is the only country in the world that ISIS fears. Apparently, ISIS is not intimidated by the U.S. nor the U.K., because ISIS believes they can defeat their ground troops.
ISIS has not been open about this weakness, and has even made threats against Israel and Jewish people in its propaganda videos.
So, if Israel is the only country feared by ISIS, why aren't they fighting ISIS?
Because they don't pose an immediate threat that needs to be countered ASAP
ISIS isn't a tangible current threat to Israel's existence.
They are definitely a threat to Syria or Iraq strategically. They pose varied levels of threat to other Middle East countries. But they don't have the military capability to attack Israel as a fighting force, not anytime soon.
Additionally, they aren't an ideological threat. DAESH's main ideology is about confronting "Rome" - Christian Western states are its main opponent.
They aren't the highest tactical threat either
Yes they would probably love to launch a terrorist attack against Israel; but they are far less likely to do so than Palestinian Authority or Hamas or Hezbollah or Islamic Jihad.
Israel has finite resources (actionable assets, political capital, budget, time); and those resources are far better invested in countering the above threats.
They don't have a broad base of support among Palestinians, because Palestinians are already committed to existing movements. Commingled loyalties (a new counter-terrorism term for people who are influenced by both ISIS and another extremist group) are possible, but ISIS doesn't offer all that much to a radicalized Palestinian that Hamas, Islamic Jihad or Hezbollah would.
Because Israel has nothing tangible to gain by fighting ISIS
As noted above, ISIS is low on Israel's threat level, so there's no threat reduction to achieve
Israel won't get any positive side effects from doing so.
Western liberals who already sympathize with non-ISIS terrorists won't change their opinion. Arab countries populace won't change their opinion either.
There are tangible downsides to fighting ISIS for Israel
It will piss off Saudis, Turkey and other anti-Shia block Sunni countries who are either indirectly allied with ISIS, or at the very least benefit from ISIS fight with Iran, Heznollah and Al-Assad who are their enemies.
It will immediately be spinned off by western MSM and definitely Arab media as "Evil joos attacking Muslims" (as evidence, witness Western media coverage of the current situation: when a Palestinia terrorist attacks Israelis, and is killed, it's immediately spun off as "Palestinian killed", not "Palestinian tried to kill Israelis and gets killed in self-defense")
It will potentially harm the current anti-ISIS coalition which includes Arab/Muslim countries.
Same thing happened with Gulf War I, when USA was concerned that Israel attacking Iraq will shatter their coalition with Arab states and thus prohibited Israel from even responding to SCUD missile attacks, never mind joining the coalition.
It will take finite resources away from countering more tangible threats to Israel (Hamas, Islamic Jihad, Hezbollah, PA)
At this point, ISIS' main tactical enemy (or one of them) is Hezbollah, so attacking ISIS will backfire on Israel in that it will "help" Hezbollah indirectly. They more they fight ISIS in Syria, the less they pay attention to attacking Israel.
