This is a tough question that is made especially difficult by two competing and conflicting motivations and desires:
- The desire to avoid encouraging and cementing hatred by suggesting that such hatred is innate or unavoidable or to blame Christianity.
- The desire to avoid brushing the long history of Christian anti-Semitism under the rug or to normalize and give a free pass to such content.
The shortest, direct, and honest answer that I can give you is that:
- History is not destiny; religions evolve over time, and though there is anti-Semitism to be found in various Christian canonical texts as well as in the works of prominent Christian theologians and in the history of Christianity, this does not mean that such hatred is innate, that Christianity need accept such hatred, or that these problematic elements cannot be de-emphasized or selectively re-interpreted (as many religions do with their problematic texts, including Judaism).
- At the same time, however, the fact is that there is a long history of Christianity not just being anti-Semitic but being a major force in the spread and instigation of such hatreds. And this is just taking into consideration the element of the kind of hatred that results in overt violence, totally ignoring the cultural appropriation angle (which, given much more severe forms of anti-Semitism, is often not discussed).
So, no, it is not inherently anti-Semitic; one can be a good, devout Christian and also not have an ounce of anti-Semitism. At the same time, there is a long history of anti-Semitism in Christianity. And while interfaith relations have greatly improved, some of these religious sources of anti-Semitism continue to generate anti-Semitism in many cases. And, in discussing overlapping texts and mythologies borrowed from Judaism, it is not uncommon for the line between cultural appreciation and cultural appropriation to be crossed (such as when some Christians tell us how to interpret our own texts rather than merely sharing how they, themselves, interpret those texts, with respect for our beliefs).
Related answers:
- My answer to Can the roots of antisemitism in Europe and the Mediterranean basin be traced back to the troubles and conflicts the Roman Empire had with the Jews, or is it a more recent phenomenon dated to after the hegemony of Christianity?
- My answer to Do you think Islam and/or Christianity are culturally appropriating Judaism? Or is it cultural appreciation? Or neither? Why?
- My answer to Does anti-Semitism come from ancient Rome?
- My answer to Why does antisemitism exist?
- My answer to Why can antisemitism be found among so many diverse cultures?