Answered by Sayyidi Habib Umar bin Hafiz (may Allah protect him and benefit us by him)
What should we do if our Shia friends invite us to one of their gatherings on Ashura?
We tell them that there are sunnahs which the grandfather of Sayyiduna al-Husayn taught us to implement on this day. If there is anything prohibited that takes place in the gathering, such as people hitting themselves or cursing the Companions, then we cannot attend. This goes against the Sunnah of the Prophet and the Ahl al-Bayt. If not, it is fine to attend merely to remember al-Husayn. We do not involve ourselves in anything that will cause dissension.
Some people make false claims that Ashura is a day of sadness in Tarim and that this was the way of Imam al-Haddad, but this is completely false. Such people only have to witness what takes place in Tarim on that day.