But then, who is the neighbour whom we are supposed to love or care for?
Interpretations vary widely and wildly. Take at one extreme the sectarian Essenes associated with the Dead Sea Scrolls. Their gloss on "thy neighbour" is a fellow member of one's sect. In their sectarian reading of the scripture, all outsiders are by definition wicked, and an Essene has an obligation to hate them. So "love thy neighbour" is transformed in a cultivated cult of hate toward the world.
On the other pole we find the old rabbi Ben Azzai who sees the commandment to love (care) as extended to all one's fellow human beings. It is not surprising that those who espoused the Jewish universalistic approach such as Moses Mendelssohn and Herman Cohen, adopted this interpretation of "your neighbour". But this universalistic reading of the verse is far from being the standard interpretation among Jewish comentators.
A far more typical reading of "thy neighbour", shared by no less authority than Maimonides, regards "thy neighbour" as confined to fellow Jews only.