Cohen Hallal

Shoud a Cohen whose father does not observe the Torah and commandments and married his mother when she was divorced follow the laws of Cohanim (priests)?

If it is certain that she was married according to the Jewish law in her first marriage, and she was definitely divorced, he is not subject to the laws of Cohanim. However, if there is doubt whether her first marriage was with kosher witnesses and it is not certain that she was married according to the law, and therefore it is not certain she is considered a divorcee, he should be stringent and behave according to the laws of priesthood as a stringency.

Shulchan Aruch, section Yoreh Deah, chapter 373, paragraph 2: 'Even a blemished Cohen is warned against becoming impure, but a hallal (invalid Cohen) and a daughter of a Cohen are allowed to become impure.'
And the Aruch HaShulchan wrote in Yoreh Deah, chapter 373, paragraph 4: 'When a son of a Cohen is born from a possible divorcee or a possible prostitute and a defiled woman, which is a biblical doubt, we go with stringency in all matters and these laws were clarified in Even HaEzer, chapter 7.'