I think this is an incorrect understanding. I think I'd agree that truth and love are inseparable, but what do you mean by "truth"? Having the right ideas or interpretation of something? I don't think that's what that means. Even if someone has a completely bogus interpretation of a Bible passage, that does not mean they are separated from truth, let alone love.
Interpretations of the Bible, and there is not one thing that anyone says about any passage of any scripture that is not an interpretation, are relative to the person, and none are or can ever be absolute. They are dependent on what understanding of the mind the person has, what their culture is, what their values are, what their education is, what their stage of development is cognitively, and what their stage of development is spiritually. It's all relative to where they are at. There is no such thing as an "absolute interpretation".
Those that pick up the Bible and point to the words and claim, "This isn't me saying this, it's God saying this!", are in fact interpreting what they are able to see with where they are at, and are assuming that because their minds understanding it a certain way, that that is the only one true understanding. That is simply incorrect. That's an interpretation as well.
But to "truth". In John where it says God is Spirit, and those who worship him must worship in spirit and in truth, Jesus is not speaking of having a correct Bible interpretation!
The context makes no sense. How does having a correct mental idea correspond with "God is Spirit"? The context is speaking of the truth of the heart, to those who worship in spirit. Worship in spirit is an act of the heart, where you set aside your ideas of what you think you know. So "truth", to worship in spirit and in truth, is about the purity of the heart. It is about pure intent, a clean conscious, clean hands. It is about sincerity. It is certainly not about "right ideas". God judges the heart, not "correct ideas". God is not known through "correct ideas".
So no, you certainly are not separated from love because you make mistakes in reading the Bible.