SJS, I thought he was differentiating between jews & non-jews. Jews have an issur of Lo Sikrevu (which includes maaseh chiba) and would be Yeharog V’al Yaavor. Non-Jews are not included in this prohibition. It would still be forbidden if it were a maaseh chibah, but for different reasons, and less stringent. Still forbidden. Just not Arayos. (This too, would be subject to debate).
I am conjecturing that he is more wary of not calling shaking hands a maaseh chiba when dealing with yeharog v’al yaavor, and willing to permit it – with a non-jew – when the issue is more lax (though still forbidden).
But there is no difference between religious and irreligious jews. That is curious. An Irreligious Jew would be equally stringent; the fact that he is not yet religious is irrelevant to Halacha.
Could you ask him? I’m genuinely curious.