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Non-Catholics are not forbidden to participate in a Catholics Mass. They can participate, of course, in fact, we welcome it.
A Non-Catholic Christian may participate in a Catholic Mass, but not in all its parts. Let me explain.
We begin by signing ourselves with the cross saying, "In the name of the Father, and of the Son, and of the Holy Spirit." (Matthew 28:19) It is a reminder of our baptismal vows, as well as our identity - that we are of the Triune God.
The priest than calls us penitence, beating our breast three times. (Luke 18:13)
We sing a praise song "Glory to God in the Highest" which we know by heart, since it is the only praise song we sing. (Luke 2:14) My wife, who is not Catholic, has already committed it to memory. No projectors required.
Everybody sits to listen to the Word proclaimed. Bringing your own Bible is fine, but faith comes from hearing. (Romans 10:17)
First reading - usually taken from the Old Testament.
Psalms - the congregation responses to the cantor.
Second reading - usually taken from the Letters of Paul.
Gospel - taken from the gospels.
The priest gives a homily - a verbal instruction or exhortation from what was read. After which, we recite the faith - the Nicene Creed.
Then comes the prayers for the Eucharist. At this part, Catholics kneel while Non-Catholics can prefer to sit. After the prayers, we all sing the Lord's Prayer. (Matthew 6:9–13)
During the Communion, Catholics receive the body of Christ in queue while Non-Catholics cannot participate.
Concluding prayers and we are all dismissed.
I feel that I am lucky because I was brought up in England where we never considered ourselves being Catholic and Protestant - we were just Christians. I really appreciate this because I feel very comfortable partaking in communion in churches of both denominations. I believe we must do as God wishes, not what the vicar tells us what to do. I have always been very welcome in my local Catholic church.