Question

1.
In Yoreh De’ah 139:11 it is explained that the garments of priests, when they come to serve idolatry, are permitted for benefit, and this is not considered an accessory of the offering, nor its ornamentation,
since the priests wear them for their own adornment and not for the adornment of the idol
(even though they think/say otherwise).
 
With all the myriads of distinctions, obviously separating the two utterly,
is a gartel in the end for the honor of the one wearing it and not for the honor of God / the prayer, even though people say/think otherwise?
 
2.
 
Once I visited the shtiebel of some rebbe.
Of all the people praying there, he and his sons were the only Hasidim in the area; everyone else was Lithuanian, Sephardi, etc. There was some friction whenever he wanted to drag out the prayers, kiddushim, and so on a bit.
The worshippers came assuming it would be late, light, short, and to the point,
and he founded the place so that it would be Hasidic…
 
One time he put up a note on the cantor’s stand saying that the prayer leader must wear a gartel…
That started some fun…
Someone went and added in writing that this only applies to someone whose underwear elastic snapped, because if there’s elastic then that’s the gartel…
Was the rebbe right, or were the worshippers?
 
3.
Does someone who doesn’t usually wear a gartel have some special reason to do so at least on the Sabbath?