I have been with my partner for 19 year's but we are not married. I started going to church three years ago, but my partner isn't a believer. Some in the church say that in the eyes of God we are married and, therefore, I should be baptized. However, others say I should be properly married before I can get baptized. My situation isn't going to change anytime soon. What should I do?
Sex does not make a couple married. See: Am I married because I did sexual acts with my girlfriend? In a similar way, going to church or claiming to believe while going against Christ's law doesn't make you a Christian. "Do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived. Neither fornicators, nor idolaters, nor adulterers, nor homosexuals, nor sodomites, nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners will inherit the kingdom of God" (I Corinthians 6:9-10).
You are currently living a life of fornication. Being a Christian is about giving up sin. "Then Peter said to them, "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit" (Acts 2:38). Getting baptized without repenting of your sins is meaningless, so either move out or get married. "But I say to the unmarried and to the widows: It is good for them if they remain even as I am; but if they cannot exercise self-control, let them marry. For it is better to marry than to burn with passion" (I Corinthians 7:8-9).
You are incorrect that your situation cannot change. You can change today if you are determined to live righteously before God.
If you are with a group that pretends that fornication is acceptable to God, you are with the wrong group. Find a congregation that supports the truth.