Two things are apparent from this article and its comments:
(1) The opinion that Messianic Judaism is “deceptive” or a “false claim of Jewishness” isn’t rooted in any sort of public statement or representation that MJs make make; it’s rooted in the belief that Messianic Judaism in and of itself is false, not Jewish, and that no MJ can be Jewish. We could have flashing neon chartreuse disclaimers at our synagogue doors saying WARNING: WE BELIEVE AND PROFESS THAT JESUS IS THE MESSIAH and it would not stop these accusations.
(2) A major portion of mainstream Judaism (or at least diaspora Judaism) simply does not and will not recognize MJs as Jews or our movement as legitimate–let alone the gospel of Yeshua’s messiahship as true. This state of affairs isn’t based on anything MJ synagogues should be doing or not doing, or who we are and are not. It’s just the current condition of the world in this generation, absent some great move of God.