Sure! Anon, this is a question that comes up a lot, and I’m not expert, but here’s what I know:

-Martha Kane and Jacob Kane were siblings

-The Kanes are established as Jewish in canon (including Jacob)

-Kate is Jewish, which, according to halachic interpretation, assumes that her mother was Jewish at the bare minimum (but that her father likely was Jewish as well)

-Martha, being Jacob’s sister, would also be Jewish (barring a weird half-brother situation, or that he converted at some point)

-The above exceptions would be unlikely considering the Jewishness of the Kane name, “Jacob”, etc. 

-At the bare minimum again, since Judaism is technically matrilineal (more about this later) and the Kane family line is Jewish, any of Martha’s children would also be Jewish

-Bruce Wayne would halachically be Jewish

Now, all of this hinges on Jacob Kane being Jewish by birth and the Kane family being Jewish overall. But there are also some additional clues:

-Kate’s family was intentionally made Jewish, in a nod to Jewish creator Bob Kane, whose family was also Jewish

-Martha and Jacob’s generation usually married within Judaism by tradition (this has changed a lot in the last few decades) and marriage into another faith was generally frowned upon. 

-The above makes it unlikely Jacob married into a Jewish family unintentionally (i.e., Kate’s mother being Jewish was important to Jacob as a Jewish man)

-Jacob is a commonly-given name to Jewish men

-Martha marrying outside the faith would explain why Bruce was not necessarily raised Jewish (in this retcon, at least)

Hey? Everyone keeps arguing about matrilineal Judaism. What does that even mean?

-This comes up a lot in Jewish Batman discourse. Matrilineal Judaism is a remnant of Biblical times, where Judaism could only be confirmed if the mother was Jewish (assuming the father was not present, etc)

-Certain sections of Judaism hold this strongly, including Conservative, Orthodox, Reform (to an extent) and some other traditions

-For a long time, and still somewhat to this day, it was frowned upon to marry a non-Jewish man (i.e., Jews tended to marry Jews)

-Patrilineal Judaism (Judaism passed down by the father)  is slowly being more accepted, as well as other discrepancies (adoption, Jewish grandparent, etc)

-Some traditions still don’t necessarily view someone as Jewish unless they practice Judaism (had a bar mitzvah, converted, etc) but this is rare, largely because of the “one drop” rule in the Holocaust, and modern aliyah standards of Israel. 

-When folks in the fandom talk about Batman in the context of matrilineal Judaism, they’re usually referring to the fact that, if Martha Kane was Jewish in any way when she had Bruce, he would technically be Jewish by birth in the eyes of many rabbis, regardless of his own practiced religion or atheism. 

-Like I said earlier, all of this hinges on if Jacob Kane was Jewish by birth. I.e., that Martha and Jacob’s mother was Jewish. 

I believe that canon has been established enough where we can assume that Jacob Kane was in fact Jewish by birth, that he married a Jewish woman, and had a Jewish child (Kate). 

I don’t believe this retcon intentionally made Bruce Jewish. Again, some would argue that he’s not really Jewish, as he’s never practiced or recognized the religion in canon. 

However, Judaism is tricky. It’s an ethnic group, a religion, and a cultural tradition, all amassed into one messy blob. It’s likely, if Martha was raised Jewish, that there were still some vestiges of Jewish cultural practices in how she raised Bruce (celebrating some holidays, traditions, or observances) unless she explicitly chose to ignore them. 

All in all, I would say it is very likely that Bruce is technically Jewish. More likely than not. An accident? Yes. But a good one for all of us Jewish fans.