The Prophet (peace be upon him) urged both man and woman to seek a religious partner, as stated by hadiths. This is because the religious person will not wrong his partner, rather he or she will praise the good doing, forgive mistakes, be helpful and supportive, and always with good manners.
A man said to Al-Hasan, a great Muslim scholar from the successors of the Companions of the Prophet, “A group of men proposed to my daughter, should I marry her to any of them? Al-Hasan said, “To the one who fears Allah most. If he loves her, he will honor her, and if he does not love her, he does not mistreat or humiliate her.”
Sheikh Muhammad S. Al-Munajjid, a renowned Muslim scholar, said,
“A Woman is urged to choose a man who is religiously committed and of good character, because the Prophet (peace and blessings be upon him) said: “If there comes to you one with whose religious commitment and character you are pleased, then marry (your female relative under your care) to him, for if you do not do that there will be tribulation in the land and great mischief.”
He adds, “If no religious man proposes to a girl, she is permitted to marry the one who is not so religiously committed as long as he is a Muslim and does not have anything that would get him out of the fold of Islam.”
Thus, the issue is somewhat proportional; if this man is completely negligent of the rituals of Islam, i.e., does not pray, fast, etc., and commits major and minor wrongdoing or the acts that violates his belonging to Islam, you are not advised to go on marriage with him. But, if he is not so but commits some mistakes as it is the case of every human being – to err is human – then there is nothing wrong with you get married to him.