Dbeda Forum

If they're both not religious, they can, some people do.
That said, any child born out of a Jewish woman is recognized as a Jew in Judaism.

According to Judaism, it's not permissible.
According to Islam, it's permissible. Muslims are permitted to marry Ahlul Kitab (people of the books), which means the Jews and the Christians provided the children will be trained as Muslims.

Allah knows the best

They are adults, if they're both liberals, they could cope well.
However, do they plan to have children? That's where the main question lies, it could be tough if they plan to have children, Judaism only recognizes a child as a Jew if the mother is Jewish while Islam leans more on the father's side.

They wouldn't be thinking of getting married if they both take religion so seriously. They should follow their hearts and heads, I know the two religion might not be in support, but they could arrange a court marriage if that makes them happy.

Any two people in love can get married with or without following the norm, social or religious standards, we have seen many cases.

I think your second question is the most important. It is permissible for a Muslim man to either marry a Jewish or Christian person.

From what I know, Judaism doesn't recognize intermarriage, some Jews do it anyways.

Now, if they eventually get married, the main issue will be their children's religion.
In Islam, children are to follow their father's religious lineage and in Judaism it's the opposite, i.e children go with their mother's religious lineage.

Therefore, I don't think it's advisable.

Can a Muslim man and a Jewish woman get married?
Is it permissable in both religion.