1.) The Bible teaches that employees are to submit to their employers with “fear and trembling, in singleness of [their] heart, as unto Christ; not with eyeservice, as menpleasers; but as the servants of Christ, doing the will of God from the heart; with good will doing service, as to the Lord, and not to men” (Ephesians 6:5-7).
It likewise teaches:
"Let as many servants as are under the yoke count their own masters worthy of all honour, that the name of God and his doctrine be not blasphemed." (1 Timothy 6:1)
"Exhort servants to be obedient unto their own masters, and to please them well in all things; not answering again." (Titus 2:9)
"Servants, be subject to your masters with all fear; not only to the good and gentle, but also to the froward." (1 Peter 2:18)
Since believers are commanded to submit to their employers as to Jesus Christ, to strike, walk out on, speak evil of, disobey, undermine, or provoke discontent against their employers is to rebel against Jesus Christ. These commands apply not just to godly employers but to evil ones as well (1 Peter 2:18). You do not bargain with Jesus Christ. You submit to Jesus Christ. The Bible requires a similar sort of obedience to your employer. Employees who are treated poorly are to cry to God (James 5:4), who will give wicked employers eternal punishment (James 5) as well as being able to apply righteous punishments even in this life, but as an individual employee the command is: “He [the employee] doth not resist you [the employer]” (James 5:6). This command to cry to God and show sacrificial love and non-resistance to employers, even wicked ones, is diametrically opposed to the beliefs of labor unions.
2.) Furthermore, the Lord Jesus Christ taught in the Sermon on the Mount (Matthew 5-7) that love to all should be the basis for the Christian's actions, rejecting the union idea of the class-struggle; Christ likewise rejected the materialism that is involved in union membership, instead teaching that the saints must seek the kingdom of God and His righteousness first; and Christ rejected the principle of force and coercion that is too often involved in union membership.
3.) Christ also specifically taught individual bargaining rather than collective bargaining for laborers (Matthew 20:2, 15).
4.) The Bible teaches that those who are part of the kingdom of God and those who are part of the kingdom of this age (cf. John 1:12; 8:44; Ephesians 2:1-10) are radically different. When the Christian recognized his status as a hell-worthy sinner, repented of his sin and any confidence in religious rituals or good deeds, and trusted in the saving work of Christ on the cross alone, he was born again (John 3:3). Those who have experienced this miraculous change have different aspirations, ways of thinking, paths in this life, and eternal destinies from those who have not, and Scripture forbids the born again from assuming an unequal yoke with those who are not in the path of God’s kingdom (2 Corinthians 6:14-7:1). These facts require Christians to refrain from joining or financially supporting labor unions.
5.) Finally, Christians must not be part of an organization that supports, lobbies for, donates to, or promotes causes that the Bible condemns. Unions spend millions and millions of dollars advocating for the legal murder of preborn children. When you give money to the union, you are supporting ripping helpless infants limb from limb while they face excruciating pain without the pain killers given to dogs and cats. You are supporting sodomy, although God says it is an abomination and He rained fire and brimstone on those practicing it (Genesis 19). You are supporting the persecution of Christian and other religious business owners and attempting to force them to violate their consciences and their duties to God. You are contributing to them having to choose to bow to the rainbow Mafia or to lose their businesses (Matthew 25:40, 45). You are violating huge numbers of Biblical principles about civil government.
Even secular people in the United States, whether in right-to-work states or states that limit one's freedom to work, cannot be forced to join unions to keep their jobs, nor can they be forced to pay full union dues. In non-right-to-work states, those with religious objections to union membership can opt out of the union and not pay the union a single penny, based on Title VII of the Civil Rights Act and principles affirmed in the First Amendment and reaffirmed in Janus v. AFSCME. (Please note that I am not a lawyer and I am not giving legal advice.)
If Jesus Christ is your Lord, then you must not bow the knee to a labor union. Do not join one, and if you are part of one, get out. If you need help in leaving, contact the National Right to Work Foundation.