I disagree with many of your presumptions.
As Naga put it, Israel combats antisemitism just by existing. It is an important idea in Zionism, the founding ideology behind Israel, that other nations cannot be trusted to look after Jewish minorities and so the real way to end antisemitic persecution is to found an independent Jewish state where the Jews can exist as a safe majority, protected by their own military and security arrangements and make their stand on the world stage as a united thriving people.
That said, countries like Iran and certain nations in the Arab world are very key in funding antisemitic terrorist organizations and spreading hateful anti-Jewish propaganda. Israel, as well as the rest of the civilized world, isolates such nations, not just due to antisemitism, but due to their general backwardsness like stoning apostates from Islam to death. Turkey has become such a nation too, at least on the antisemitism front, but then have you ever wondered why they were never let into the EU?
Israel DOES fight antisemitism, even abroad, by funding educational campaigns, countering the propaganda out there, denying entry to known individuals who have been known to engage in antisemitic activities or with antisemitic organizations (which the US, UK and other countries also do to an extent), as well as Mossad hits on Nazi fugitives and senior Islamic extremists, maintaining the world's largest collection and database of Holocaust evidence, survivor testimonies and largest Holocaust museum so that there is no question from educated people over the integrity of reports of this historical genocide. The list goes on.
Now let's talk about antisemitic Islamic extremists who support Jeremy Corbyn in the UK, backwards pro-Trump neo-Nazis, the KKK etc. These are minorities in their respective nations, which the host nations, being civilized countries, already monitor and tackle. The presence of these antisemitic minorities should not command Israel to shut off and sanction entire nations which actually are important strategic allies, trading partners and general forces of furthering Western democracy and morality in this bitterly cruel world.
To also add some food for thought, there will always be some people who will hold antisemitic feelings, which is disgusting, but allowed by freedom of thought and freedom of speech. Nobody can go around thought policing these people, which would be equally as disgusting. The solution is to instead promote education of future generations and isolate the antisemites of this world, as well as monitor any potentially law-breaking activities they may do and actively debunk their "arguments". Israel plays its part well.