لَا إِكْرَاهَ فِي الدِّينِ (No compulsion in religion) applies to those from whom Jizyah is accepted: the People of the Book and foreign religions.
It does not apply to the people to whom a Prophet is directly sent to. The Quran recounts of several nations who were utterly destroyed for rejecting Allah's Messengers and signs. The disbelievers in Noah's time weren't expelled and told to take their idols with them ... they were drowned in a flood which wiped every trace of them.
As for the Arab polytheists: a Messenger walked in their midst, the Quran was sent in their language and miracles were shown to them, angels fought in battles against them ... they had no choice to reject, nor did the Prophet accept anything from them less than Islam (Refer to books of Seerah e.g Ibn Kathir) .
وَقَاتِلُوهُمْ حَتَّىٰ لَا تَكُونَ فِتْنَةٌ وَيَكُونَ الدِّينُ كُلُّهُ لِلَّهِ ۚ فَإِنِ انتَهَوْا فَإِنَّ اللَّهَ بِمَا يَعْمَلُونَ بَصِيرٌ
And fight them until there is no fitnah and [until] the religion, all of it, is for Allah. And if they cease - then indeed, Allah is Seeing of what they do.
— Quran 8:39
فَإِذَا انسَلَخَ الْأَشْهُرُ الْحُرُمُ فَاقْتُلُوا الْمُشْرِكِينَ حَيْثُ وَجَدتُّمُوهُمْ وَخُذُوهُمْ وَاحْصُرُوهُمْ وَاقْعُدُوا لَهُمْ كُلَّ مَرْصَدٍ ۚ فَإِن تَابُوا وَأَقَامُوا الصَّلَاةَ وَآتَوُا الزَّكَاةَ فَخَلُّوا سَبِيلَهُمْ ۚ إِنَّ اللَّهَ غَفُورٌ رَّحِيمٌ
And when the sacred months have passed, then kill the polytheists wherever you find them and capture them and besiege them and sit in wait for them at every place of ambush. But if they should repent, establish prayer, and give zakah, let them [go] on their way. Indeed, Allah is Forgiving and Merciful.
— Quran 9:5
قال رسول الله صلى الله عليه وسلم " امرت ان اقاتل الناس حتى يقولوا لا اله الا الله. فمن قال لا اله الا الله، فقد عصم مني نفسه وماله، الا بحقه، وحسابه على الله
Allah 's Messenger said, " I have been ordered to fight with the people till they say, 'None has the right to be worshipped but Allah,' and whoever says, 'None has the right to be worshipped but Allah,' his life and property will be saved by me except for Islamic law, and his accounts will be with Allah."
— Saheeh Bukhari 2946
Regarding what ruling applies in Islam to idolatrous subjects of the Islamic state, after the death of the Prophet, there are three views: The view of the Malikis is that they will become Dhimmis and Jizyah will be accepted from them. The view of the Hanafis is that non-arabs will be become Dhimmis and Jizyah will be accepted from them. The view of the Shafis is that Jizyah will not be accepted from idolators and only from People of the Book and Zorastrians.
قال الشافعي رحمه الله : لا تقبل الجزية إلا من أهل الكتاب خاصة عربا كانوا أو عجما لهذه الآية ، فإنهم هم الذين خصوا بالذكر فتوجه الحكم إليهم دون من سواهم لقوله عز وجل : فاقتلوا المشركين حيث وجدتموهم . ولم يقل : حتى يعطوا الجزية كما قال في أهل الكتاب . وقال : وتقبل من المجوس بالسنة ؛ وبه قال أحمد وأبو ثور
Imam Shafi said: Jizyah will not be accepted except from the people of the Book (Jews and Christians) be they Arab or non-arab. The evidence is this verse because these have been specifically separately mentioned. Hence it will only apply to them and not to others since Allah says فاقتلوا المشركين حيث وجدتموهم ("Kill the mushriqeen wherever you find them") (9:5) and did not mention حتى يعطوا الجزية (till they pay Jizyah), as he mentioned about the people of the book. And Shafi said further that Jizyah will be accepted from the Zoroastrians since it is proven from the Sunnah. Similar was said by Imam Ahmad and Abu Thawr ...
— Tafsir Qurtubi
وذهب مالك والأوزاعي : إلى أنها تؤخذ من جميع الكفار إلا المرتد
Malik and Awzai's saying that it will be accepted from all disbelievers, except apostates
وقال أبو حنيفة : تؤخذ من أهل الكتاب على العموم ، وتؤخذ من مشركي العجم ، ولا تؤخذ من مشركي العرب
Abu Hanifa's saying is that it will be accepted from the Ahle Kitab, both arab and otherwise, and from the non-arab mushriqeen, but will not be accepted from arab mushriqeen.
— Tafsir Baghawi
وتوضع الجزية على أهل الكتاب والمجوس ... وعبدة الأوثان من العجم ... ولا توضع على عبدة الأوثان من العرب ولا المرتدين
[Hanafi view] Jizyah will be accepted from the people of the book and the magians ... and the worshippers of idols from the non-arabs ... it will not be accepted from the idol worshipping arabs nor apostates
— Al-Hidayah Fi Sharh Bidayat al-Mubtadi (English Translation)
When they pay Jizyah and are Dhimmis they are legally protected, are allowed to continue on their religion and their places of worship and idols are not permitted to be destroyed.