The Bible says to treat your neighbor as you would want to be treated.
Who is the neighbor?
Is EVERYONE equally the neighbor?
Should we be, indiscriminately, generous to EVERYONE in need?
I believe that when the Torah was written, "neighbor" referred to fellow Israelites. That's the only people who were around. For me, it applies to all who are around me, most of whom are not Jews.
The following is just my own thoughts. I think that charitable responsibility works best when it flows from the inside out.
My primary responsibility is my own care and survival; no one is going to take better care of me than me.
After that comes my responsibility towards my family, first my immediate family, then extended family; it is my job to be sure i.e. that my children are loved, fed, housed, educated, etc -- it's simply my job as a parent.
My ultimate extended family is the Jewish people. They get many of the benefits that family gets, for example, if I loan money to a fellow Jew I don't charge interest because they are family. I'm more inclined to work out civil matters between us than go to court, i.e. if necessary use a mediator and the Jewish beit din system.
After that comes my responsibility to my community. The closer to home, the greater my responsibility. IOW the homeless in my own city take priority to the homeless across the country. But my responsibility is still there, in varying gradations to county, state, nation, and the ultimate community, the world.
So yes, I have a responsibility to feed the starving child in Africa if I can, by i.e. supporting policies that will oust dictators that corrupt the system, will allow in national aid, or aid from the UN, etc. But this responsibility pales in comparison to my responsibility for the hungry child that lives on my own street.