We have nothing in common.

Literal

Us [to-には] anything-[emphatic-も] common-point [subject-が] not-exist.

A double-negative construction. 何も + ない = 'nothing.' 共通点 ('common point, commonality') is a Sino-Japanese noun. The 僕らには structure uses には to mean 'as for us, (there is nothing).' An honest admission of incompatibility.