This well known and well learned rabbi on his popular facebook page promotes intermingling and cross mixing of Jewish and Islamic ideas and believes that Islam is a welcome reformation of rabbinical Judaism. He has also has many articles there showing commonality between both Judaism and Islam. Hence is it allowed for rabbis and general population to practice both Islam and Judaism simultaneously like how this rabbi seems to be doing. Also even his Jewish followers consider him well learned rabbi, So the question is does Judaism permit practicing all Islamic activities? and can Islam be welcomed as a reformation in Judaism?
He writes on linkedin page:
Before the religious courts, I propose that Muslims are derived from the God-fearers mentioned in the Torah. To do this, I argue historically, that the people referred to as Muslims (before the Qur'an came) are identical with the God-fearers mentioned in the Torah and related works.
further info: alsadiqin.org/en/index.php?title=Main_Page
Note: There might be other rabbis supporting Judeo-Christian intermingling like Jews for Jesus, but here the case is different as Islam is not avodah zarah and conversion to it does not demand death .