All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
We mentioned the difference between wearing clothes that have some of the slogans of disbelief, such as idols, which is a way of promoting them and a kind of approval, and the mere pronunciation of their names when speaking in fatwa 350620. So please refer to the above fatwa, as it answers your question.
Also, there is an obvious difference between the ruling on worshiping at a place where a mosque was originally built for worshipping Allah alone and for establishing the remembrance of Allah and a place where nothing was built for this purpose. Allah honored Makkah, and its mosque was basically built for the Tawheed of Allah (i.e. for worshipping Allah alone without associating any partners with him) and to establish the remembrance of Allah.
Allah says (what means): {And [mention, O Muhammad] when We designated for Abraham the site of the House, [saying], "Do not associate anything with Me and purify My House for those who perform Tawaaf [circumambulation] and those who stand [in prayer] and those who bow and prostrate.} [Quran 22:26]
Then the idolaters came and brought idols to Makkah. But when Allah enabled His Prophet to conquer Makkah, the Prophet removed those idols and returned Makkah to its former state.
As regards Buwaanah, it is a place like all other places where there is nothing that the Shariah favored with more virtue and advantage, and the Muslims did not build a mosque there for worshiping Allah, so it remained a neglected place. Then when someone wanted to sacrifice a camel there, the Prophet asked him whether there has ever been a worshipped idol there or a festival of the Jaahiliyyah (Pre-Islamic Era of Ignorance), because if that was the case and someone comes to slaughter there, then this may be a reason for bringing back that practice of the Jaahiliyyah.
Had the Shariah honored that place from the beginning and made it a place of worship as Makkah, or had the Muslims built a mosque in it for the worship of Allah – as the Companions did in Taa'if, when they demolished the Laat idol and built the mosque of Taa'if near that place, then the Prophet would not have asked about that. So there is an obvious difference between the two matters.
Allah knows best.