Gadol; the gemara says one is not allowed to save the life of an oved avodah zara, even if paid to do so, except in a case where hatred of jews would become increased (mipnei aivah). Today’s goyim who believe in monotheism are not subject to that prohibition and one may save their lives regardless of the aforementioned, though it definitely is not an intrinsic obligation.
As it happens to be, the halacha i quoted above – ain mefakchin alav es hagal, that we are prohibited from saving the lives of ovdei avodah zara, should be proof enough that darchei sholom was never intended to mean more than promoting peace with goyim (mipnei aivah is different, it allows that which would normally be a worse sin, darchei sholom allows a lesser sin, though this is my own chidush and I’m not going to stand by it should it be disproven)
If saving their lives or healing them is assur, feeding them if they’re hungry should be no different, absent darchei sholom in the latter and aivah in the former