Well that depends, of course, on what you mean by anti-Semitic. The New Testament does not advocate any sort of mistreatment of Jews. However, it is quite clear that (normatively speaking) Jews, like anyone else, must come to know Christ to be saved. And nowhere does it demand a special view toward the modern state of Israel. If you are a Christian, base your support (or lack thereof) for Israel on your politics. Do not base it on erroneous interpretations of prophecy. Supporting Israel because she is the lone democracy in the region is defensible. Supporting Israel because her enemies tend to hate us is defensible. Supporting Israel because the bible tells us to is just plain wrong.
Many Christians believe that the founding of modern Israel was in fulfillment of prophecy. God, this argument goes, has unfulfilled promises made to the Jews. This is not true. The founding of Israel was, as all things are, ordained by God. He wasn't surprised by the development. But it does not complete any outstanding biblical prophecy. As for any unconditional promises remaining unfulfilled: that's the empty set. There were many promises that God made with the condition of obedience—those promises are null and void. But the unconditional promises were satisfied:
43 So the LORD gave Israel all the land he had sworn to give their forefathers, and they took possession of it and settled there. 44 The LORD gave them rest on every side, just as he had sworn to their forefathers. Not one of their enemies withstood them; the LORD handed all their enemies over to them. 45 Not one of all the LORD's good promises to the house of Israel failed; every one was fulfilled. (Joshua 21:43-45)
Extreme pro-Israel Christians such as John Hagee, author of the hideous In Defense of Israel (which I may review at a later date) are simply and seriously mistaken. He claims that the bible calls Christians to do much more than pray for the state of Israel. He is right and wrong—the bible does call us to do much more, it calls us to proselytize, i.e., preach the gospel, to the Jews. He is wrong because proselytizing the Jews is the one thing he does not demand of his followers. He prefers to stand side-by-side with the political leadership of Israel to further Israel's political agenda. As stated earlier, this may be a defensible position based on your political views. But Hagee, and many other Christians, falsely claim the bible as their mandate.
Back to the question of anti-Semitism. Have you ever actually read what Paul (who everyone knows loved the Jews and even offered his own salvation if they could be saved) had to write about unconverted Jews? After being repeatedly attacked on his missionary journeys, Paul wrote:
13And we also thank God continually because, when you received the word of God, which you heard from us, you accepted it not as the word of men, but as it actually is, the word of God, which is at work in you who believe. 14For you, brothers, became imitators of God's churches in Judea, which are in Christ Jesus: You suffered from your own countrymen the same things those churches suffered from the Jews, 15who killed the Lord Jesus and the prophets and also drove us out. They displease God and are hostile to all men 16in their effort to keep us from speaking to the Gentiles so that they may be saved. In this way they always heap up their sins to the limit. The wrath of God has come upon them at last. (1 Th. 2:13-16)
By any modern sensitivities—these words taken from scripture (and not out of context) would be considered anti-Semitic. Paul is literally calling the Jews "Christ killers."
(Aside: the wrath of God is no doubt reference to the impending end of the Jewish age in AD 70, when the Temple was desecrated and destroyed, over a million Jews killed, many enslaved, the rest mostly scattered—the end of Israel and of the sacrificial system. In my opinion, that was the last time you have any prophecy about God's wrath on a political entity—and it denoted the end of the transition period between the old and the new. God, according to my reading of scripture, no longer deals with nations but rather with those in his church and those not.)
Some extremely pro-Israel Christians also argue that taking the position that Jews cannot be saved without accepting Christ is also anti-Semitic. Well, it is not anti-Semitic; it is the proper position for Christians to take; although there is something important to remember.
What I mean is this: as people we can base our judgment only on the visible fruits of others. We are called to treat as Christians those proclaim acceptance of the power of Christ's shed blood to pay for their sins. And we are called to treat anyone who doesn't as an unbeliever. Because of our inability to do anything else, God has told us: pay attention to the externals and act accordingly—but the actual Book of Life is off limits. We will not bat a thousand using this approach.
Scripture, read carefully, tells us that nobody comes to the Father except by the Son. But while this is obviously strongly correlated with those who can present a testimony, in truth it is slightly different. Coming by the Son means presenting oneself before the Father cloaked in the righteousness of Christ. Could Christ offer the protection of His righteousness to some who don't follow the normative route to salvation? Who am I to say no? God will have mercy upon whom he will have mercy. I am instructed, in Matthew 7, to treat those who deny Christ as unbelievers and those who don't (and back up their claim with deeds) as believers. But conspicuously absent from that instruction is a guarantee that by this methodology I'll perfectly distinguish the saved from the lost.
With infants and the mentally handicapped we understand this intuitively. We all are Calvinists when it comes to dead babies. While it doesn't affect my actions toward them in any way, I have the same feeling about Jews, Moslems, (both of which should be proselytized) and the millions who never hear the gospel. If they don't convert, I don't expect that they are saved, and I don't treat them as if they are saved, but I do hold out a hope for any individual that in God's sovereign plan he will have mercy upon them, and I do remember that I have no say whatsoever when it comes to the question of who gets covered by the righteousness of Christ.