Hmm, I'm not sure about this connection. Politics derives from the Greek
polis or city (as in metro-polis), which in turn has cognates to the Greek
poly, many (as in, polyamorous). Politics is intimately connected to the
city as a state of social organisation, in which strangers live together, and have to negotiate how to live with one another. One can further refine the political by noting that it is often set in contrast to the space of the family or the home (the
oika), in which relations of kinship rule. Negatively speaking, political relations are those which are not kinship relations:
"The rise of the city-state meant that man received 'besides his private life a sort of second life, his
bios politikos. Now every citizen belongs to two orders of existence; and there is a sharp distinction in his life between what is his own (
idion) and what is communal (
koinon)'. It was not just an opinion or theory of Aristotle but a simple historical fact that the foundation of the
polis was preceded by the destruction of all organized units resting on kinship, such as the
phratria (brotherhood) and the
phyle (clan/tribe). (Arendt,
The Human Condition, embedded quote from Werner Jaeger,
Paideia).
Polite, as far as I can tell, has a Latin root, which at the very least, post-dates the Greek, and
if it is related to it, would be derivative of it and not constitutive, as it were. Still, the idea of accommodating differences - I think I'd prefer to say negotiating, which has a less conciliatory air - seems about right, even though I quibble about the etymology.