The abuse and slander against Shias will not stop even if they stopped performing Tatbeer, as it was continuing for centuries against them because of their commemoration of the tragedy of Ashura. The reason behind this is obvious: because it places the role of the Muslim caliphate into question since the authorities killed the grandson of the Prophet, Imam Hussien (peace be upon him), in such a terrible way only fifty years after the death of the founder of the religion, the Messenger of Allah (peace be upon him and his holy progeny).
The act of Tatbeer is not a general practice of the Shias on the day of Ashura since those who perform it is limited in number with respect to the population of Shias that commemorate the tragedy every year. From that, one can conclude that the slander against the Shia is not simply due to them performing Tatbeer.

As the act of Tatbeer and other kinds of symbolic actions are performed to propagate the right principal and express emotions towards it, then it is religiously recommended from this side. Yes, it can be prohibited because of secondary reasons, like if it causes prohibited harm, public disadvantage or other similar reasons. There is no set criterion for such prohibition as it differs from place to place and from time to time. It can also be different because of difference in personal perspectives.
We ask Allah Almighty to guide us and all devotees in all of that as we only depend on Him.

Religious rituals that Shias perform to mourn the tragedies of the Imams of the Ahlulbait (peace be upon them) and to present the oppressions that they suffered are recommended. However, it is obligatory to avoid what causes harm to the soul or the body. If it does not result in harm, it remains being recommended. One should avoid performing them in a place where the reputation of the Shias is damaged.

Mourning Imam Hussein (peace be upon him) as an expression of sadness and grief for the tragedy of Karbala is recommended. Some believers during such ceremonies bleed. The fact that our blood is Najis does not affect this expression of grief. Yes, if the body or clothes become Najis by blood, or any other Najasah, one should make it Tahir before offering the prayer.

It is prohibited to make the mosque Najis. It is not prohibited to make other places Najis, especially when they are going to be purified afterwards.

The narrations do not mention that the Imams (peace be upon them) shed their own blood because of their sadness and grief for what happened to Imam Hussein (peace be upon him). However, it was reported that they wept and that they encouraged crying loudly, like the supplication of Imam Jaffer Al-Sadiq (peace be upon him): "my Lord, have mercy on the wailing that is raised for us." It is also reported in Ziyarah al-Nahiyah which is narrated from Imam Mahdi (may Allah hasten his reappearance): "I will mourn you day and night, I will weep for you blood instead of tears, in grief for you". Such narrations and others indicate the greatness of this tragedy.