Probably not very much, with the caveat that religiousity is not a single dimension, nor is prejudice.
The best survey I'm aware of was done by Pew. It assessed how positively or negatively Americans felt toward various religious groups.
Atheists and agnostics, on average, gave a slightly less warm rating of Jews than did Christians. This might be a significant difference, but the effect size is small: 68 degrees for Protestants versus 63 for religiously unaffiliated.
As such, there might be a slight correlation, but the difference seems small.
While I think this is a decent proxy for anti-Semitism, it's not perfect. Anti-Semitism, like any kind of prejudice, encompasses a constellation of beliefs and opinions, not all of which are related to mere affiliate feeling. For instance, some premillenial dispensationalists may feel warmly toward Jews but belief that they will have to accept Christ, a belief which some characterize as anti-Semitic. Other groups, such as Messianic Jews, Black Hebrew Israelites, and Christian Identitarians, may define the word Jew much more narrowly but not necessarily identify as Jewish on the survey, which could tilt the numbers a little.
Further, which religion a person adheres to may be relevant. Religious Jews (and non-religious Jews) view Jews more positively. Although the survey didn't have enough Muslim respondents to get results, it's possible that religious Muslim respondents will either lack premillenial dispensationalist arguments, or be influenced by perception of Israel's actions, and thus have a lower score on average. Some religious Hindus might be influenced by opinion of Pakistan and by perceptions of Jews as being against Islam. And so forth. Conversely, if the survey had split out pre-millennial dispensationalists from the larger evangelica pot, it's possible that they'd be even more warm toward Jews than "white evangelicals."