Imam ibn Katheer wrote:
“Ibn Is-haaq said, ‘Muhammad ibn Jaʻfar ibn Az-Zubayr narrated that the (Najraan) delegation came to the Messenger of Allaah, sallallaahu ʻalayhi wa sallam, in Madeenah and entered his masjid wearing robes and garments after he had prayed the ʻAsr prayer. They accompanied a caravan of camels led by Bani Al-Haarith ibn Kaʻb. The Companions of the Messenger of Allaah who saw them said that they never saw a delegation like them after that. When their time of worship came, they stood up to perform their worship in the Prophet’s masjid. He, sallallaahu ʻalayhi wa sallam, said, ‘Let them (worship),’ and they prayed towards the east.‘”
[Tafseer Ibn Katheer]
The Fatawa at Islamweb #319777 says:
We could not find a chain of narration for this story except for this one on the authority of Ibn Is-haaq which has some narrators missing in its chain of transmission indicating its weakness.
In any case, if this report is proven authentic, it does not indicate that it is permissible for the non-Muslims to enter the masjid and perform their prayers therein without restrictions. On the contrary, it is restricted to a clear benefit such as inviting them to Islam.
In the story of Thumaamah when he was taken as a prisoner of war before his conversion to Islam, he was detained in the masjid and tied to one of its columns. The story was cited in Saheeh Al-Bukhari and Saheeh Muslim. Some scholars held that the reason that he was tied to a pillar in the masjid was to make him see the Muslims while performing the prayer and reciting the Quran.
Read the story of Thumaamah (رضي الله عنه) here(read both the narrations)-
https://sunnah.com/muslim/32/70
Conclusion: Since the story of the Prophet ﷺ inviting the Christians of Najran and allowing them to pray in The Masjid according to their customs is not authentic, we can not use that as a proof to allow Non-Muslims to enter the Masaajid and pray as they will and wish.
The authentic story of Thumaamah bin Uthal (رضي الله عنه) shows us that Non-Muslims may be allowed into The Masjid so that they see the worship of the Muslims and that softens their hearts towards Islam.
Allah says in The Quran:
(وَأَنَّ الْمَسَاجِدَ لِلَّهِ فَلَا تَدْعُوا مَعَ اللَّهِ أَحَدًا)
And [He revealed] that the masjids are for Allah, so do not invoke with Allah anyone.
[Surat Al-Jinn 18]
-Compiled by Abu Muaaz Mohammed Manna
Saheehus-Seerah 