First, let us be clear about what anti-Semitism is. By definition, anti-Semitism is a form of racism or racial hatred. It involves the stigmatization of a particular racial or ethnic group. It may also be combined with anti-Judaism, but not necessarily (the latter has to do with a prejudice against the Jewish religion).
When we are discussing first-century A.D. Judaism, we need to bear in mind that there was no one orthodoxy by which all forms of Judaism could be measured. As the great Jewish scholar Jacob Neusner has said, there were various forms of early Judaism (he has even spoken of 'Judaisms'). The fact that there was vigorous debate, polemics, and propaganda fired across the battle lines between first-century Jews should not be taken to reflect anti-Semitism. One could be opposed to a particular form of early Judaism--for instance, as the Qumranites were opposed to the religion as practiced in the temple built by Herod the Great--and not be in the least anti-Semitic. (Though the Qumranites were themselves only a small portion of the Jewish population, like the Pharisees who made up perhaps 5% of the population, they seem to have had impact and influence on the nation far beyond what one might expect.) Opposition to a particular form of early Judaism should not be taken to indicate anti-Semitism.
Secondly, the Gospel writers, with the possible exception of Luke, (who in my view was a Gentile God-fearer or synagogue adherent before he became a follower of Jesus), were all Jews. They would be very surprised to hear someone call them anti-Semitic, since they were Semites themselves. Some other early Jews may well have seen them as bad or even apostate Jews, but they would not likely have accused them of being anti-Semitic. We must view the polemical remarks we find in the Gospels' Passion and Easter narratives within the context of the larger intra-Jewish debate in that era about what true Judaism should look like.
It goes well beyond the evidence to suggest that the author was implying that the Jewish people as a whole or as a race were opposed to and wanted to crucify Jesus. The text simply will not allow such a conclusion. Jesus' followers, as well as his opponents, were all Jews, and part of an intra-Jewish struggle for the soul of the Jewish people.
At first glance, the saying in Matthew 27:25 may seem to be of another and more anti-Semitic nature, but in fact it is not. This verse must be read in light of Matthew 27:20, which says that the chief priest and some elders persuaded the crowd that was there present to ask for Barabbas. It is again this same crowd which is referred to in 27:24, and therefore the reference to "all the people" in verse 25 can only mean this same crowd which was present on that occasion, who had been whipped into a frenzy by some authorities. The most one can say about this is that some Jews present on that day wanted to see Jesus executed. This hardly amounts to anti-Semitism, so long as Matthew 27:25 isn't taken out of context and misused. Very few scholars, including Jewish scholars who study the New Testament, would argue that even Matthew 27:25 when read in its larger context is intended as an anti-Semitic remark. That it has been misused this way in subsequent Christian history is shameful, and indeed sinful, but the text itself should not be interpreted in an anti-Semitic way.
So where does this leave us? James Carroll and others are certainly right that the Christian Church has a lot of anti-Semitic history to repent of, but it is not helpful in dealing with that process to make false accusations about the writers of the New Testament, who themselves were Jews. Indeed, it hinders the process of repentance and healing that needs to happen as the Jewish Christian dialogue goes forward in the 21st century.