I had my first bagle when I came to Poland first, 8 years ago.
Bagels are not a Jewish food. Only in the US they think it's Jewish. In Israel it's looked at as an American food.
In fact isn't much of Polish/Jewish cuisine similar?
You are probably only familiar with Ashkenazi Jewish cuisine, which is heavily influenced by Polish cuisine, but there are lots of different kinds of Jewish cuisine, and in Israel they all come together.
it seems that there is so much influence on each other, between Poles and Jews
I don't know about real cross-cultural influence, but there is i think a mutual fascination, sometimes attraction and sometimes repulsion. Why am I on a Polish forum if I wasn't drawn somehow to Poland? Why are there Jewish style restaurants in Krakow?
But I think in the next generation or two the relationship will fade away – no love, no hate.