Hi Johanika. Great question, and certainly an issue that all worship leaders will face.The bible calls us to speak the truth in love. I think we are called to be extra sensitive to the artistic personality, because they are so easily wounded or offended. Obviously we don't want to do that.
That said, if you were responsible for the church finances and a person who couldn't manage basic math wanted to "help out" would it be a dilemma for you to keep them out of the church books, or would you affirm that you are being a good steward of what God has given you to manage? Likewise, if a person wanted to preach, but had no training in the scriptures, would you permit them to teach?
Nowhere in the Bible does it say that worship team should be open to everyone who thinks they should participate. The whole purpose of the audition process is to validate that the person applying for the team has been musically gifted by God, has the spiritual maturity to participate, and is willing to submit to the authorities God has placed in the church.
Over the years, I have had many, many people that felt they would like to be on worship team, but had no musical gift. So how do you discharge the responsibility for leading the worship team when that may mean you have to tell someone that they cannot participate?
I think it helps to remind yourself that God has placed you in a position of responsibility, and given you charge over the worship team, if that is your duty. The bible tells us that there is no authority except the authority established by God, and he who rebels against God's authority, brings judgement upon themselves. Additionally, the bible tells us that we are God's workmanship, created in Christ Jesus to do good works, which God has prepared in advance for us to do. In other words, you are over the worship team because God has prepared you for the job, and appointed works for you to discharge. You are serving the Master, as He has called you to serve. Sometimes that means having a great time in worship with the body of Christ, and sometimes it means sitting down with someone to have a difficult talk. Gotta eat the spinach along with the Salmon fillet.
It is never easy, or enjoyable to tell someone that they do not meet the requirements of worship team. I suggest you meet with the person and review gifts as described in 1 Cor 12 and Romans 12. Paul give us a wonderful dissertation on gifts. He uses the analogy of various parts of the body to demonstrate diverse gifts. The scripture is also affirming in that it clearly says that everyone has been given gifts. It also discusses what happens when a part of the body wants to be something that it was not designed to be.
Let the person know that you greatly appreciate their desire to serve. Tell them specifically what they are not able to do (play adequately, remain on pitch, blend with other vocalists, lifestyle issues, whatever). Although there is a tendency to want to gloss over this in hope of no hurt, don't do it. Being specific with a particular issue, helps the person understand what they can work on to address the problem. Leave the door open for them to work on their deficiency, and then re-apply. Voice lessons or music lessons can work wonders, so leave them the opportunity for a second chance.
Don't leave the door open for gossip. Immediately address the worship team letting them know that so-and-so will not be participating on the team at this time, but may become part of the team in the future, if that is what the Lord wants for them.
Set a time limit before you meet with the person, so that you have a grace opportunity for ending your meeting. Do not allow comparisons with other people on the team to enter into the conversation. That just invites difficulty.
As far as a person participating on a worship team in another church, that is a non-issue. What ever standards the other church may set for participation on worship team is of no matter. You are not charged with managing the other worship team, just yours. You set the standard that God calls you to set. It matters not what someone else does.
Hope this helps you.