In the eyes of halacha, who is in greater violation of the prohibition of blasphemy, an idolator or an atheist?
Whichever is worse, is that the case by both Jew and Non-Jew?
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Rambam in Guide for the Perplexed 1:36 writes as follows:
How great, then, must be the offence of him who has a wrong opinion of God Himself, and believes Him to be different from what He truly is, i.e., assumes that He does not exist, that He consists of two elements, that He is corporeal, that He is subject to external influence, or ascribes to Him any defect whatever. Such a person is undoubtedly worse than he who worships idols in the belief that they, as agents, can do good or evil.
(Friedlander translation, my emphasis)
Rabbi Tovia Singer seems to say that idolatry is worst than atheism. Saying that should not be mistaken as saying atheism is the preferred path.
I am an Orthodox Jew. Nevertheless, atheism can purify much in religion according to Rabbi Kook. Kook wrote that G-d needs atheists:
”Because atheism cleanses the dross of ‘petty religion,’ the narrowness and provincialism of established Jewish religion that frequently becomes arrogant, rigid and judgmental. We need these people, these atheists, whom seek to befriend.”
Thus, atheism is a good path to rational religion (though not the only one).
 Religious Zionism of Rav Kook by Dr. Pinchas Polonsky
 Essay by Rabbi Alan Brill