It isn’t just Fundamentalist Christian groups which are fussy about women’s dress codes. Both Muslims and Orthodox Jews have similar attitudes.
There are numerous Bible passages regarding the subject of modesty which, not referencing thongs specifically, make it clear that any manner of dress which would be too revealing is forbidden. I’m surprised that you failed to find any mention of this. Just putting the word modesty into any decent Bible concordance would net a fair number of relevant passages. I’ll try to hunt up a few when I get some spare time.
Each group has their own interpretations of that but the basic idea is to not dress in a sexually suggestive manner.
It would seem to me that in the situation you describe that the problem is less the thong itself as it is the fact that the clothing covering it is so tight as to reveal its contours.
If a lady were wearing a loose pleated skirt obviously it wouldn’t make much difference whether it was a thong or regular underwear underneath since it wouldn’t be obvious.
Also of interest along these lines recently, I was reading an article about Yoga pants being the current item being regarded as too revealing.
And there are some Pentecostal churches which require members to wear either dresses or skirts. Pants or slacks of any type are absolutely verboten.
IMHO, a lot of this places too much of the responsibility upon a woman for the control of mens sexual impulses. A certain degree of modesty makes sense but most people have the good common sense to not dress for church in the same way they would for going to a club or a concert.
But treating women like children with the icky picky regulations employed by most conservative groups (whether Christian, Jewish, or Muslim) is pretty unfair and ridiculous. Just my two cents worth.