The mosques in Islam are the houses of worship (See also How should Muslims treat houses of worship of other Religions? on houses of worship of other religions). But we also know or have learnt from the history that the Prophet () and the sahabah have been teaching or counselling with each other etc. inside them for what we may call worldly matters (marriages, counselling on how to prepare for a battle, choice of a leader for an expedition or a preacher etc.).
Nevertheless some acts that clearly are halal are not allowed in a mosque (or at least in some mosques) as stated in the Qur'an and sunnah:
... And do not have relations with them as long as you are staying for worship in the mosques. These are the limits [set by] Allah , so do not approach them. Thus does Allah make clear His ordinances to the people that they may become righteous. (2:187)
... And do not fight them at al-Masjid al- Haram until they fight you there. But if they fight you, then kill them. Such is the recompense of the disbelievers. (2:191)
(Comment: This might be a specific case!)
The Messenger of Allah (ﷺ) said: If anyone hears a man crying out in the mosque about something he has lost, he should say: May Allah not restore it to you, for the mosques were not built for this. (See for example in Sahih Muslim)
Could we therefore say that mosques in Islam have a sacredness?
What kind of normally halal things or acts are not allowed in mosques?
