Q. Why can’t Jews and non-Jews pray together?
If this means that all peoples will share a common liturgy and theology it is not something of this pre-messianic world. In the world of history we are divided by concepts, conscience and commitments that make joint prayer impossible.
There is a conventional argument, “But surely we all believe in the same God?”
The fact is that though God is central to the beliefs and prayers of all monotheistic faiths, we have different ways of understanding His nature and His will.
When a Jew says HaShem echad – “The Lord is One”, his words have their own connotation. When he says, S’lach lanu Avinu ki chatanu – “Forgive us, our Father, for we have sinned”, his concept of sin and forgiveness is distinctive.
When he says, Ana HaShem hoshi’ah na – “We pray, O Lord, grant salvation”, he means “salvation” in a particular sense.
A Jew can join in a prayer such as “Lord and Giver of all good, we praise Thee for our daily food”… but even then he would quietly or otherwise add his own Jewish b’rachah.