The first Christians were all Jews.
I don’t know what religion Muhammad was before he founded his own religion of Islam. If he was a Christian, though, this would not mean to me that a Christians for Islam movement deserves to have any credibility within the Christian faith.
Christianity and Judaism have been separate religions under the understanding of both religions for nearly 1800 years. It is only in the last 40 years that a group of Christians who had converted some Jews (e.g., Moishe Rosen) to their faith set out to adopt a name that they thought would make more Jews comfortable in abandoning their own religion and joining theirs.
It is nothing more than a frontal attack on Judaism and an effort to convert them to the Christian faith.