Can a woman that commits adultery, drinks and uses Gods name in vain and lies claim to be a Christian at church on Sunday morning? Also how long can she go to the altar and lie and say how sorry she is for what she has done all through the week? Who does a woman like this serve God or Satan?
A person can do anything he wants and claim to be a Christian. But claiming to be a Christian doesn't make one a Christian any more than my claiming to be President of the United States would make me so. All that one's own claims to Christianity can do would be to help or harm the cause of Christ, depending on one's actions.
I can not presume to stand in the place of judge and determine anyone's sincerity in their repentance. That is God's prerogative. We are told "by their fruits shall you know them" (Matt 7:20), but it is possible to be sincerely sorry for sin and yet commit it again.
On the other hand, Paul tells us that immersion (baptism) is the point at which we start a new life and that we are then dead to the old life of sin (Romans 6). Particularly, he says, "Likewise reckon ye also yourselves to be dead indeed unto sin, but alive unto God through Jesus Christ our Lord. Let not sin therefore reign in your mortal body, that ye should obey it in the lusts thereof. Neither yield ye your members as instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God. For sin shall not have dominion over you: for ye are not under the law, but under grace. What then? shall we sin, because we are not under the law, but under grace? God forbid. Know ye not, that to whom ye yield yourselves servants to obey, his servants ye are to whom ye obey; whether of sin unto death, or of obedience unto righteousness?" (Rom 6:11-16) If we continue in the same lifestyle of sin that we did before we were immersed, then it is likely that we weren't baptized for forgiveness of sins, but simply got wet. Christianity is walking in the light (1 John 1:7), not just claiming to have been saved. We prove our salvation by the way we live.
One other passage may apply. Paul told us how to deal with those in the church who are sexually promiscuous. "I wrote unto you in an epistle not to company with fornicators: Yet not altogether with the fornicators of this world, or with the covetous, or extortioners, or with idolaters; for then must ye needs go out of the world. But now I have written unto you not to keep company, if any man that is called a brother be a fornicator, or covetous, or an idolater, or a railer, or a drunkard, or an extortioner; with such an one no not to eat. For what have I to do to judge them also that are without? do not ye judge them that are within? But them that are without God judgeth. Therefore put away from among yourselves that wicked person." (1 Cor 5:9-13) Do not keep company with such a one within the congregation, until they change their actions. Then accept them back if they show a true change of life.