I'm having hard time understanding the definition of idolater. It is easy for me to recognize for example that who prays a statue is an idolater. But what about other monotheistic religions? Are christians and muslims considered idolaters?
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This has been addressed elsewhere on this site.
Islam is certainly not idolatry. They believe in a single, non-corporeal God; we just differ with them about exactly who received prophecy from that God and what that prophecy was.
As for Christianity -- Unitarians are not considered idolaters. Something like Catholicism or eastern Orthodox churches get trickier as there are physical images involved (though a single, non-corporeal God is also in the picture), so the rabbis debate it.
Let me stress again that you have no right to go out hurting people or damaging property because of "idolatry." This discussion of "idolatry" comes up most often with Judaism's strict laws against benefiting from idolatry -- for instance, if there is a mosque for sale, I can buy it and turn it into a restaurant (or synagogue, for that matter). If there is a Hindu temple for sale, many rabbis will say that it was built to house idols and therefore I am not allowed to use the building.