In the US, conservative is almost synonymous with politically right-wing. In Israel, someone conservative – שמרן or שמרנית – refers to the personality trait meaning of the word, while ימני (masculine) or ימנית (feminine) is someone right-wing.
He’s very much a conservative, preferring to go on what’s sure.
Instead of calling him a conservative, we could describe him as such, saying:
In Israel, the Jewish Conservative Movement is not called by the literal translation התנועה השמרנית , but rather התנועה המסורתית – the Traditional Movement.