sechel: The Baal shem tov himself traveled to be mikarev Jews, and sent shluchim, so did all the rebbes. If anything how it’s only chabad, many yrs ago it was every rebbe going around himself and sending shluchim to be mikarev Jews. It was maybe a bit different cuz most Jews in those times were just simple and ignorent and needed chizuk, to be taught what to do, but even then they deal with people totally off as seen in all the seforim.
They most certainly did not travel to non-frum Yidden to be mekarev them because the concept of ‘non-frum Yidden’ had not really come about at the time. As you yourself say, they traveled in their areas to encourage people who were erlich and yirei Shomayim, but who needed chizuk. Yes, there is the occasional story of meeting meshumadim and the like – there is a famous story of the Besh”t and the bishop – but those incidents were to save Yidden, not merely to be mekarev the meshumad himself.
In truth, I don’t know the extent of kol Yisrael areivim, which is why I did not bring any argument to indicate that we are not responsible for all the Yidden who don’t put on tefillin. But the fact remains, that it was never done in the past in any community, so the rule of kol Yisrael areivim must not apply to that type of activity. I don’t know why, but it seems very clear to me that that is the case.