Most definitely. For good, or for ill.
Exactly. Just as you would like me to take your word for things pertaining to Judaism, I can tell you about Christianity from a first-hand perspective.
You're welcome. Back in 1981, I was one of those who helped make it so. I cannot tell you the hours spent contending that Messianic shuls should not be merely churches where we put up Jewish art on the walls. I was also one of those arguing that Jewish missions should not entail merely "getting a profession", and then "send them to a local church".
The modern Messianic Jewish leadership that is so highly valued by some strike me as conveniently short-sighted and ungrateful for the level of effort and support they have received from many, many Gentile Messianics.
This is a posture that has existed since before "Messianic Judaism". We have always called it "Hebrew Christianity". That term described Christians who happened to be of Hebraic descent and culture.
Up until around the early 2,000's, MJ was on a track towards developing its own independent theology and culture, apart from the Christian churches. Then it got side-tracked.
Not the case in my experiences. More like, people who are uninformed of the difference are more relaxed. People who know, know the differences make a difference.
Yes. You are referring to those who follow, "Hebrew Roots of the Christian Faith"--the Two Housers and Sacred Namers, and contrarians who find paganism behind every tree and under every rock. They are against everything and everybody, Christian, Jewish, or Other.