Can Ephraim love Yehudah (Jew-dah), but dislike their Rabbinic system?

YES! Yes, they can!

Except, much of Ephraim (10-Israel) doesn't know the difference between WRITTEN Torah and Rabbinic Halakha, so Ephraim has frequently and historically found themselves literally throwing "the baby out with the bath water". How many times have Ephraimite nations exiled Judah from their countries? Martin Luther is a prime example of an Ephraimite who first reached out to the Jewish people, but increasingly became enraged by the Talmud and rabbinic resistance to the Messiah (if you read and compare his earlier writings with his later, you'll notice the progression of anger).

On the flipside, Ephraim has largely not known who they are for roughly 2700 to 2000 years, but are now awakening to their identity, but ironically, Judah (the Jews) won't allow Ephraim to enter modern Israel because Ephraim will largely not accept Judah's Rabbinic System nor reject their Messiah. Even so... the Prophets say Ephraim will return. And all the more, it looks like Judah needs Ephraim to return. And it is fascinating that much of Protestant 10-Israel expresses the desire to fight with Judah against her enemies. Yet the enemies of Ephraim and Judah are largely found within... compounding the problems on both sides.

Seems we're at a bit of an impasse. And interestingly, יהוה is brought the most honor and esteem when Jacob is at an impasse, because יהוה is the One to bring the solution and/or deliverance.

Where is Eliyahu, the Prophet of יהוה when you need him?