Can we be united in prayer? Are there any of the large groups of believers in Jesus that would object to praying with other denominations, non-denominations or sections of Christianity?

Example: Catholicism, Protestant, etc?
The header question is actually a different subject from the body of the question. The body of the question is about 'large groups' and their possible 'objections'.
The head question is a fundamental issue :

Can we be united in prayer ?

I am answering this basic question. I am assuming that the 'we' is persons who confess the name of Jesus Christ among their fellow human beings and that the 'we' is persons who 'depart from iniquity'

That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved. [Romans 10:9, KJV]
Let every one that nameth the name of Christ depart from iniquity. [2 Timothy 2:19, KJV]


Jesus Christ, himself, said :

I will build my church. [Matthew 16:18, KJV.]

It is Jesus Christ who builds the church, in any generation. Humanity on earth does not and cannot do this. How could it be possible ? Shall the Church exist, anywhere and at any time, in the absence of he whose name it bears ?
What on earth would be the point ? And what kind of 'church' would it be ?
So, no, we cannot be united 'in prayer'. It is not prayer that unites. It is the living presence of Jesus Christ, the Son of God, who unites. That is to say (in the physical absence of him who rose from the dead and ascended into heaven) the Living presence, in the Person of the Holy Spirit, who (alone) conveys the real presence and the Living Person of the Son of God.
Peter said to Jesus of Nazareth :

Thou art the Christ, the Son of the living God. [Matthew 16:16, KJV]

and Jesus said to Peter :

... thou art Peter, and upon this rock I will build my church [Matthew 16:18, KJV]

This relationship is what unites Jesus and Peter : a relationship in which each one knows (and names) the other one. They know one another, in a spiritual way. And this unites them in a spiritual union. Which union is as strong and as permanent as rock.
The 'rock' is a relationship with Jesus Christ, a relationship not of flesh and blood (see verse 17) but of Spirit and by faith and by the revelation that Jesus Christ of Nazareth is, as Peter confesses at that very moment of time :

... the Son of the living God.

This is what unites. Not humans gathering together, themselves, and deciding to pray together. That will be a united gathering of disparate human beings. And, especially, it will be a gathering of persons who are deliberately setting aside some very real issues and some very pertinent matters of righteousness.
In other words, a casting away of integrity in order to be 'united'.
But that is not how Jesus Christ builds the church that is really his and the church that truly is worthy of the description : The Body of Christ.
Because what genuinely unites true believers in Christ, one with another, is the real and living and present - Person of Jesus Christ, himself.
And it is He, himself, who gathers them together.