What is the ruling of Islamic law concerning how to deal with those who believe that one who abandons prayer out of denial is an infidel, and then their error becomes clear, and with those who display behaviors not committed to religion, and is it obligatory to correct their misconceptions?

"Verification is necessary when transmitting fatwas. Anyone who transmits an incorrect fatwa must correct it. The statement that scholars have unanimously agreed on the disbelief of one who abandons prayer is not entirely wrong; rather, it is understood as abandoning it out of denial, or it refers to the consensus of the Companions, who unanimously agreed on the disbelief of one who abandons prayer, even without denial. A number of scholars have narrated their consensus.

Therefore, your not qualifying the matter with denial is not problematic, unless you meant later scholars. These scholars did not unanimously agree on considering one who abandons prayer a disbeliever unless they denied its obligation. A student of knowledge is advised to dedicate themselves to acquiring knowledge, maintain good companionship, and call sinners and advise them without engaging in lengthy discussions."