Thai profanity never has religious theme. Sex-themed words (equivalents of whore, son-of-a-bitch, motherfucker, cunt-face) are commonly heard, but only in times of great anger.
Milder cusswords in very common use (though still considered off-limits to foreigners) are:
ฉิบหาย - /chip hai/ = ruinous, very
ไอ้เหี้ย - /ai hia/ = water monitor lizard
Animal names are in common use as cuss words, e.g. the word for rhinoceros or the water monitor.
(Water monitors are commonly seen where I live; many call them by a word that translates as “creature of silver and gold” to avoid the taboo name.)
There are euphemisms in use for ‘lie, liar’ to avoid the term
ตอแหล - /tor lae/ = ‘lie, liar’
which is a fighting word.