Messianics vs. Liberal Judaism, What's the Difference?

I’ve been interested in how classical, “Orthodox,” Judaism differentiates between non-halachic Jewish movements and Messianics/Jews for Jesus, even though both of these groups diverge from Rambam’s (Maimonades’) 13 principles of faith, which is seen in traditional circles as a litmus test.  In my opinion, part of the answer can be found in Melachim B (Kings II.)  Compare 15:28, “And he [King Pekach of Israel] did what was evil in the eyes of the Hashem, he did not turn from the sins of Yerovam (Jeroboam,)” aka worshiping the Ba’al idol. Simultaneously, in 15:34, “And he [King Uzyah of Yehuda (Judea)] did what was right in the eyes of Hashem… however, the high places were not removed,” referring to impermissible worship at private altars in lieu of the Beit Hamikdash (Holy Temple) in Jerusalem.  It seems that worshipping a foreign God (Messianics) is seen as an abomination.  Worshipping the God of Israel in a way which is not sanctioned is seen as a correctible misunderstanding.