The root meaning of the word Christian has no problem. However, Christianity defines a new man made religion and therefore, the title Christian carries with it automatic meaning and subtext beyond it's core meaning.

It is often stated that Christianity and by inference, the Church was birthed at Pentecost. This is not only patently false, it is blasphemous when you come to understand the pagan roots of Christianity. Christianity and the church became a codified state religion around 400AD.   

Compare the two passages below. Note the bolded words. The first is closer to the original text, the second is translated to fit a particular doctrinal narrative.

The word assembly is a reasonable translation of both the Hebrew and Greek. It denoted a gathering of like minded people and in this context connected to a local Jewish Synagogue. While there may have been a few gentile converts, the vast majority of this assembly were Jews, or Gentiles who had converted to Judaism who subsequently believed in Yeshua of Natzaret. The Yeshua movement was simply a sect of Judasim at this time. There was no 'church' with a cross painted on the wall, or held high on a steeple.

The words 'messianists' and 'christian' have the same meaning as they are the same words in different languages. However, note the capital in Christian! The modern mind immediately thinks Christianity, Trinity, Codified Religion. 

What we have here in Acts is a reference to what would grow into the Messianic Movement, persecuted into near extinction in the centuries to follow. This was not the foundation of the Church and Christianity that formally took place 300+ years later under Emperor Constantine. The very basis of Christianity, clearly recorded in written history was to be a religion totally disconnected from everything Jewish and this included the Messianic Movement.  

In this context, to say Jewish, is to think the religion of Judaism.

Judaism is a man made religion While based upon the Torah, it includes laws and regulations that have come to supersede the written Torah and this is the very problem that Yeshua taught and railed against. Never did Yeshua undermine the written Torah. He did go out of His way to break the religious laws of men however. Yeshua's sect was an offshoot of Judaism restored correctly to the written Torah. He himself became the Living Torah.

'Jews' who are not Jewish This is a long and complicated story, however, it is important that we understand terms correctly. Israel is made up of twelve tribes. After the civil war at the end of Solomon's reign, the tribes split into ten and two. The northern ten tribes, (often referred to as the lost tribes) were exiled by Yehovah due to idolatry. This left two tribes. Yehudah and Benyamin. These tribes were also exiled at a later time for the same reason and taken captive to Babylon. Babylon was conquered by Persia and the two tribes were set free. The tribe of Benyamin had ceased to be a functioning tribe and was absorbed into Yehudah. (We see Shaul was of the Tribe of Benyamin, but called himself a Jew) The exiled ten tribes remained dispersed among the nations.  At the time of Ezra a tiny percentage of the tribe of Yehudah returned to the land of Israel. They thought at the time that they represented all that remained of Israel. And so, in their minds, Yehudah now represented all Israel. (What they didn't count on was God returning members of ALL Israel's tribes to the land of Israel in the last days. The days in which we now live). A true Jew is a member of the tribe of Yehudah. Yeshua was a Jew, of the tribe of Yehudah. When in exile, the tribe of Yehudah developed a man made religious solution to replace a system what was now impossible to implement without the land and the temple. This man made system became the roots of Judaism. The problem was that once able to return to the land of Israel and with a rebuilt temple, true Torah based worship was not successfully resumed  in the long term and the man made religion discarded. By the time of Yeshua, not only had Judaism developed further, the true temple worship had become so corrupt that it was barely operational. No wonder we needed a Savior!

So, we are neither Christian or 'Jewish' (meaning adherents to Judaism). Our religious system is the one instituted by Yehovah Himself. The written Scriptures are our standard. In general it is wise to bear the following in mind.

When in the Church you are taught the Bible, Right? No, you are taught Christian Doctrine.

When in Synagogue you are taught the Torah, Right? No, you are taught the Mishnah, Judaic Doctrine.

in both cases you are taught the Doctrines of Men. We are not about the Doctrines of Men, pure and simple.