Christians won't fellowship different denominations but a Muslim can fellowship at any mosque anywhere. Not true!
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There are 4 difficulties which need to be addressed.
1. Churches are just buildings and the teaching that we have to go to a particular building to worship God is not found in the New Testament. In the New Testament the word translated ‘church’ is the Greek word ‘ekklesia’ which means an assembly or congregation of people. In other words a ‘church’ is a body of believers and not a building. It is wrong to believe that a building can be consecrated by Christians as a place of worship in the same way as the Jewish Temple was. The Temple was ordained by God as a place where God would dwell with Israel. No Christian has ever been instructed by God to make a building for God to dwell in.
Those who believe the true gospel and are baptised into Christ come under a new Covenant.
Hebrews 10:16 This is the covenant that I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them;
The heart of the Christian is where God dwells.
2 Corinthians 6:16... for ye are the temple of the living God; as God hath said, I will dwell in them, and walk in them; and I will be their God, and they shall be my people.
Christ gives the following instruction about praying:
Matthew 6:6 But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly.
2. Christians are to meet together to break bread and drink wine in remembrance of the sacrifice of Christ. They do not need a special building to do this. In the first century they did it from house to house.
Acts 2:46 And they, continuing daily with one accord in the temple, and breaking bread from house to house, did eat their meat with gladness and singleness of heart,
Christian Jews continued to worship in the Temple until the Temple was destroyed. Christian gentiles were not permitted on pain of death to worship at the Temple.
3. Meeting to break bread and drink wine is an act of fellowship. Fellowship is only possible with those that believe the same gospel and hold to the same doctrines.
2 John 1:10 If there come any unto you, and bring not this doctrine, receive him not into your house, neither bid him God speed: 11 For he that biddeth him God speed is partaker of his evil deeds.
Galatians 1:8 But though we, or an angel from heaven, preach any other gospel unto you than that which we have preached unto you, let him be accursed.
4. It does not matter what Muslims do. However, you are mistaken in your idealized picture of Islam. There are 3 major sects of Islam: Sunni, Shia, and Sufi. Under those, there are more than 70 smaller groups many of which are mutually exclusive to the point of open warfare. Muslims are no better than Christians in their disunity and discord and a case may be made that they are considerably worse. People are people no matter what they profess and the nasty side of human nature intrudes into every human life and every human organization, secular or religious. Having said that, what Muslims do or don't do is irrelevant because there is only one way of salvation and that is through Christ. Those that do not believe and obey the gospel of Christ die in their sins and will not see life.
John 8:24 I said therefore unto you, that ye shall die in your sins: for if ye believe not that I am he, ye shall die in your sins.
John 3:36 He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him.
Acts 4:12 Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.
We do not go to heaven when we die, we go to the grave.
Ecclesiastes 9:5 For the living know that they shall die: but the dead know not any thing, neither have they any more a reward; for the memory of them is forgotten. 6 Also their love, and their hatred, and their envy, is now perished; neither have they any more a portion for ever in any thing that is done under the sun.
Psalms 146:4 His breath goeth forth, he returneth to his earth; in that very day his thoughts perish.
To see life we must be raised from the dead.
1 Corinthians 15:21 For since by man came death, by man came also the resurrection of the dead. 22 For as in Adam all die, even so in Christ shall all be made alive. 23 But every man in his own order: Christ the firstfruits; afterward they that are Christ’s at his coming.
We do not have an immortal soul. Immortality is a gift bestowed upon those who are accepted at the resurrection
Romans 6:23 For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.
The act of worshipping in a particular building is of no value in terms of attaining to eternal life. We will be judged on our obedience to the gospel preached by Jesus Christ and the apostles. All of which is written down in the Bible for our learning.
Those who worship God by the commandments of men worship him in vain.
Mark 7:7 Howbeit in vain do they worship me, teaching for doctrines the commandments of men.
We need to be guided in fellowship and worship by what the Bible says.
I hope you have found this helpful.
May God bless you,