Of all the people you expect to make the claim that Christianity is idolatry, who would be your last pick? Try apologetics ministries. Because they pretty much do exactly that, but in a round-about way that you're not likely to catch, but which a Jew will almost certainly catch. Have you ever heard the claim that, "the Jews don't worship the same god that Christians do because they don't worship Jesus"? Guess what: Any Jew that understands God's law will take this as an open admission that Christians serve a different god than the one that brought them out of Egypt. Of course, the same people who make such a claim will also state that Jesus is the same God that brought Israel out of Egypt. But this isn't going to help much. This would have made a great entry into my 5 Inconsistencies With Church Doctrines post.
Let's examine the first claim from the perspective of a religious Jew who has even just a basic understanding of the Deuteronomy 13 Test. A religious Jew believes he/she is worshiping the God who brought the descendants of Jacob out of the land of Egypt. This God then have the nation of Israel his law, which includes instructions on how to test a teacher. These instructions state that if anyone comes in the name of another god, you are not to listen to that teacher. Now, here comes your mainstream "Christian" apologist from a very popular apologetics ministry who claims that the Jews and Christians do not worship the same god. Do you see the problem here?
So now we have the religious Jew who believes that he/she is worshiping the God of Abraham, Isaac, and Jacob. And we have the Christian, who also believes that he/she is worshiping the God of Abraham, Isaac, and Jacob. And in one "careless" statement, the "Christian" apologist has caused both of them to believe that the other worships a false god. In other words, the apologist has caused the Jews to believe that Christianity is the epitome of idolatry! Thus the apologist has just made it that much harder. Because according to Deuteronomy 13, anyone coming in the name of another god (aka: exactly what the apologist claims every Christian is doing) is to be put to death. Obviously, not a good way to win a Jew to the Lord.
If we want to win a devout Jew to the Lord, we need to do it in a way that does not cause them to think that we are coming in the name of a different god, yet does not compromise the truth. Does such a way exist? Yes. Actually, two ways that I can think of. The first is to prove that the Jews do not, in fact, worship the God of Abraham, Isaac, and Jacob. We can do that by pointing out the more subtle definition of idolatry in Deuteronomy 13: Disobedience. That's right, Deuteronomy 13 defines obedience as serving Yahweh, and disobedience as serving other gods (aka: idolatry). Though I seriously doubt this approach will work for the simple reason that most who profess being Christian make every excuse in the apologetics book to avoid obeying God's law. Have fun winning them over by making them think you're a hypocrite. Most apologists are probably not going to use that approach anyways because they know very well the implications of Deuteronomy 13.
The second way is to prove that the God who brought Israel out of Egypt is the same God that sent Yeshua (Jesus). Or if you insist on being more picky than the original apostles on how you present things (there's something for a future post), prove that Yeshua is the God that brought Israel out of Egypt. Not only are these things true, and easily proved from just the Old Testament alone, but it also has the added benefits of (a) not making Christianity look like idolatry, and (b) not making Christians look like hypocrites.
Here's another point to consider: Upon learning that "Jews and Christians don't serve the same god" (assuming for a moment that the claim is true), did you assume that Christians serve the right god while the Jews do not? Because it can also be the case that it's the Jews who serve the right god while the Christians do not, or that neither the Christians nor the Jews serve the right god. Those who make the claim that "Jews and Christians don't serve the same god" are counting on you to make the assumption that Christians serve the right god while Jews serve the wrong god. They are also counting on you to not even consider the possibility that neither serve the right god, or to even know what it truly means to serve God.
So what does it mean to serve God? I already answered that when I referenced the Deuteronomy 13 Test. Serving God means obeying him and keeping his law/commandments. So it's those who keep God's commandments truly serve him. And this should give you something else to consider: Since Deuteronomy 13 is teaching you how to test the teachers and prophets when it defines disobedience as idolatry, it means that anyone who claims to be the Messiah must teach obedience to God's law, also called "Torah" in Hebrew, which literally means "instructions". Such a person must also himself keep the Torah. Any messiah that does not both keep and teach Torah, by definition, cannot be the son of God.
Here's another point to consider: Just because you serve someone named "Jesus" (aka: "Yeshua"), doesn't mean you serve the right Jesus, for there are many counterfeits. So how do you know you're serving the right one? You actually already have your answer: The one you obey is the one you serve (Romans 6:16). So if you put Yeshua's teaching in the Bible into practice, and obey his commandments, then you are by definition, serving the son of God. Jesus is also the example of how to obey Torah. And since he outright commanded us to obey God's law, you cannot be serving Jesus without also keeping Torah.
So if saying Christians and Jews don't serve the wrong way to evangelize, then what's the right way? Well, we already have part of the answer. Both Jews and Christians claim to worship the God of the Bible, also referred to as the God of Abraham, Isaac, and Jacob. And apologists do a very good job of showing how Yeshua fulfilled all of the "Old Testament" prophecies concerning his first coming. That's already a pretty good start. But we also need to approach the issue as if both Christians and Jews do serve the same god. Because in the mind of the Christian, Christians do serve the God of Abraham, Isaac, and Jacob. And in the mind of the Jew, Jews do serve the God of Abraham, Isaac, and Jacob.
Here comes the part that most Christians will not like: We must stop dressing Yeshua and those who were around him in that day in pagan clothing and symbolism, and dress them in the Jewish clothing of that day. For Yeshua (Jesus) was born a Jew and lived as a Jew, having Jewish parents and practicing Jewish customs in strict accordance with Torah (Yeshua did not practice any Jewish customs that were contrary to Torah). We must also stop claiming that Yeshua abolished the law, as he clearly said he did not come to abolish it, but to fulfill it (Matthew 5:17). If we no longer have to keep the law (the law was never about salvation, by the way), then Yeshua did the opposite of fulfilling the law. By the way, another thing most Christians won't like is the fact that following in Yeshua's example means doing what Yeshua did [1 John 2:6].
While there will be some success in reaching out to Jews without actually walking as Yeshua walked, you certainly aren't going to be provoking them to jealousy by hanging onto all of your Golden Calves. In other words, our effectiveness at bringing God's elect to salvation is directly tied to how we portray Yeshua. But the moment a Jew comes across a Christian apologist saying that Christians and Jews do not serve the same god is the moment that our witness to God's chosen people becomes entirely ineffective to all Christians until we can first prove that Christians and Jews do indeed serve the same God. And woe to anyone who deliberately sabotages any attempt at Jewish outreach.