Should we pray for Christian groups that hold beliefs that we disagree with and/or that do things we don't approve of? Jesus did. In John 17, Jesus didn't just pray for His first disciples, "but for them also who shall believe on Me through their word; that they all may be one."
To me, that means all true Christ-followers, in all time periods, in all nations, and in all Christian groups. Perhaps you and I also should pray for all Christians (and Christian groups), too. God wants to reach the nations. I believe that He also wants to reach the denominations.
In Luke 6:28, Jesus told His disciples to: "Bless them that curse you, and pray for them who despitefully use you." If we are commanded to do that, surely we can pray for other Christians. (Those who have ever been hurt by church know that Christians are sometimes the ones who despitefully use us.)
The book of James tells Christians to, "pray for one another, that you may be healed." Of course we can pray for individuals, but we can also pray for groups of Christians other than our own.
Here's how Paul prayed for the Ephesian Christians: "That the God of our Lord Jesus Christ, the Father of glory, may give unto you the spirit of wisdom and revelation in the knowledge of Him: the eyes of your understanding being enlightened; that you may know what is the hope of His calling, and what is the riches of the glory of His inheritance in the saints, and what is the exceeding greatness of His power toward us who believe."
So how can we pray for the Baptists, Lutherans, Catholics, Orthodox, house churches, Pentecostals, megachurch attendees, Anglicans/Episcopalians, charismatics, Methodists, Presbyterians, Dones, nondenominational, and thousands of other Christian groups? Here's a sample prayer we could use:
Father, I ask You to bless the (fill in the specific name a Christian group here). I pray that You will give them Your wisdom and supernatural revelation through Jesus. Enlighten the eyes of their understanding. Let them know and experience the hope that Christ has called them to, the inheritance that He has given them, and the exceeding greatness of His power in them.
Father, let them have the unity of the Spirit among themselves and with other Christians. May they deeply love one another and all other Christ-followers, so that the world will know that You are from the Father.
May they have a harvest of souls in their midst. Bring their nominal and/or non-born-again members and attendees to full salvation and transformation through Christ. And use them to bring multitudes of people, who have ignored or rejected Christ, to repentance and freedom in Jesus.
Fill them with your Spirit. Give them all a supernatural love for You and an all consuming passion to follow and obey Jesus every day.
Empower them to live godly lives. Renew their minds and keep them from being conformed to the world.
I ask this in Jesus' name. Amen.