When true teachers tries to work together with false teachers, two things can happen. Either the work of Christ get jammed, or the Church walks into deception.

Jesus spoke about unity.
Did he speak about unity inside a team, or was it a universal unity regardless of doctrinal disagreement?
When Jesus said that his true followers had to watch out for false teachers and false prophets that would come in His name, I guess he would also place some watchmen around us, that we should listen to?
In the book of Revelation, Jesus honors a Church that has rejected false Apostles.
Revelation 2:2
I know your deeds, your hard work and your perseverance. I know that you cannot tolerate wicked men, that you have tested those who claim to be apostles but are not, and have found them false.
It would be an insane thing to do, to let such people walk and talk like teachers inside Churches, place their hand on the flock, and let their false anointing jump onto the sheep.
Act 20:28-30
Keep watch over yourselves and all the flock of which the Holy Spirit has made you overseers. Be shepherds of the church of God,which he bought with his own blood. I know that after I leave, savage wolves will come in among you and will not spare the flock. Even from your own number men will arise and distort the truth in order to draw away disciples after them.
Should we not test all spirits, and be good Shepherds of the flock?
When Jesus told his students about the wheat and the weed, he did not promote falsehood inside the body of Christ. But He did not want his students to go and fight other groups that used the name of «Jesus».
Matthew 13: 28-29:
An enemy did this,’ he replied.
“The servants asked him, ‘Do you want us to go and pull them up?’
” ‘No,’ he answered, ‘because while you are pulling the weeds, you may root up the wheat with them.
The best example of the weed and wheat not being a part of the same team is found in these two verses:
Mark 9:39-40.
“Teacher,” said John, “we saw a man driving out demons in your name and we told him to stop, because he was not one of us.”
“Do not stop him,” Jesus said. “No one who does a miracle in my name can in the next moment say anything bad about me, for whoever is not against us is for us.
Why did Jesus say this?
Because stopping this man of doing something in the name of Jesus, would make a bad name of the Messiah in the eyes of non-believers.
Jesus will anyhow not overlook falsehood that is done in his name, as best explained in this verse.
Matthew 7:21-23.
“Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but only he who does the will of my Father who is in heaven. Many will say to me on that day, ‘Lord, Lord, did we not prophesy in your name, and in your name drive out demons and perform many miracles?’Then I will tell them plainly, ‘I never knew you. Away from me, you evildoers!’
People who minister together have to become one in mind and Spirit. There should always be unity inside teams, and even in small Churches. In lager cells and units, there is a higher risk that fake and falsehood will creep in and jam the movement. People who love power, money and fame do not seek control over small House Churches.
Keep falsehood out of the body of Christ.