Learn English – English equivalent to the Bengali Idiom ” bamon hoye chand dhorar shokh” which means wish of a lowly person to become equal to aristocratic people

LET GOD SORT THEM OUT

The OP has stated that the phrase in question, "means that one considers all the instances of some group as equally bad ... "

The meaning of the OP's phrase is about not caring, as opposed to, not knowing. Additionally of great significance, the phrase is an expression of vituperation and disdain, conveying a fundamental lack of concern or moral consideration for any who fall within this category (choose your favorite 'scapegoat') because these have been judged to be the equivalent of "feces," and there are no "grades" of feces, each and all are merely and only, "shit."

While admittedly not an exact equivalent, there is a phrase which pithily sums up the same blithe lack of moral concern and invective, “Kill them all; let God sort them out." This phrase is considered to be a derivation of "Caedite eos. Novit enim Dominus qui sunt eius", a phrase allegedly spoken by the Papal legate and Cistercian abbot Arnaud Amalric, prior to the Massacre at Béziers, a massacre in the French town of Béziers that formed the first major military action of the Albigensian Crusade. A direct translation of the Latin phrase would be "Kill them. For the Lord knows those that are His own." See, Wikipedia Caedite eos. Novit enim Dominus qui sunt eius. The phrase was possibly a misunderstood reference to 2 Tim. 2:19 which, in part, reads, “The Lord knoweth them that are his”.

I would go with "My brain is fried." I hear this frequently in everyday life (working as a scientist in southern California). I'm not sure I've ever heard anyone say "brain turned to mush," but perhaps that's a regional difference. "I'm frazzled" is probably even more common and has roughly the same meaning, but is less parallel to your yogurt-brain saying!