Hello @Francescaesse,
we had asked the Milan municipality and and they had answered us that if the guests are for free, the tourism tax is not due.
But, as mentioned here for a similar question about Rome, as a host, you need to be able to prove to the tax authorities that your guests are not paying. Therefore, some members who also have an apartment registered for short-term rentals prefer to ask for it anyway. If they do, they must then remit it and provide a receipt, to avoid any potential abuse toward the guest.
However, in principle, if your accommodation is not paid for, meaning there is no price, the tax would not be due. You can ask your Comune to verify this response.