Mosques are places designated for prayer and should welcome everyone who wants to pray irrespective of how they want to worship. Sura 2, Aya 114 says:
And who is more unjust than he who prevents people from the mosques of Allah so that His Name is celebrated there? --whose zeal is (in fact) to ruin them? It is not fitting that such people should themselves enter the mosques except in fear. For them there is nothing but disgrace in this world, and in the world to come, an exceeding torment
We should recall that although the Quran repeatedly urges people to pray, it does not specify any particular format for prayer. This is because Allah hears all prayers, irrespective of the manner in which prayers are said, and hence places designated for prayer should welcome all worshippers irrespective of how they pray.
Individual Muslims follow the rules for prayer prescribed in the madhahib (or schools of thought) of different scholars such as Imam Abu Hanifa, Imam Shafi’i, Imam Malik, Imam Jafar Sadiq and others. The followers of each imam pray differently, and at somewhat different times. Furthermore, followers of different Prophets pray still differently. All of them should be made welcome to pray in a mosque, as long as they do not disturb other worshippers.
Of necessity, each mosque is managed by the followers of one school of thought and therefore their method of prayer is the announced mode of worship in that mosque. But, the aya (2:114) quoted above reminds us that we are on the wrong path if we prevent others from using our mosques.
At this time the wisdom taught in this aya is ignored in the majority of mosques around the world. And this indicates the deep distrust among Muslims for their fellow Muslims who follow different interpretations. This intolerance is often manifested in job discrimination, economic disruption, political conflict and sometimes in violence against those who are in minority. This pervasive prejudice is a major factor in the backwardness of Muslim culture
A fundamental principle of Islam is that every religion based on the worship of God is to be respected, no matter how much one may disagree with their particular practices. A well known illustration of this principle is that when members of the Christian Najran tribe visited the Prophet (pbuh) in his mosque in Madina in the 10th hijri year, the Prophet (pbuh) invited them to perform their prayer service there. This is striking because the purpose of their visit was to argue with the Prophet (pbuh) about their belief in Trinity and Jesus as the son of God.