It is difficult to answer "how common" it is, considering that the Shi'a community worldwide is split up across many different cultures and practices all over the world. An easier question to answer is: Is this cursing a standard part and teaching of Shi'a Islam?
In general, Shi'a Muslims determine their religious duties by performing Taqleed, or referring to one of the top most-learned scholars who are considered experts in extracting religious law. A top scholar like this, known as a marja', is at a very different level from ordinary local religious scholars. There might be thousands of regular religious scholars in the world, but only a few have reached the level of marja', and out of those, only a handful have large followings around the world. When it comes to establishing religious laws, only the statement of an established marja' matters, not the opinion of any scholar of lesser rank.
One marja' among those with the most followers worldwide is Grand Ayatullah Sayyid Ali Sistani, who was asked about the issue of cursing the Prophet's companions and wives. Here is the question and his response:
The Question:
as-Salamu Alykum wa rahmatu Allah wa barakatuhu,
A video clip has been seen several times on social network web sites showing a congregation during the martyrdom of al-Imam al-Jawad (p). This group of people from the area known as al-A’dhamiyyah are shown shouting out insults upon ‘Omar, A’isha, and others. Is this type of behavior condemned by the supreme religious authority, especially since it involves the insult of religious figures of our brothers of the Sunni school of thought, and it could potentially fuel unrest amongst the people of Iraq and jeopardize peace?
The Answer:
In The Name of Allah, The Beneficent, The Merciful
This type of behavior is condemned, strongly denounced and contrary to the commands of the Imams of the Holy Household of the Prophet (p) to their followers. Allah is The Guide.
The Office of Ayatullah Sayyid al-Sistani
The Holy City of Najaf
(Source)
The marja' Ayatullah Sayyid Ali Khamenei, who also has millions of Shi'a followers worldwide, issued a similar statement (this one specifically refers to the wives of the prophet, based on the question he was asked):
“Disrespecting the pure wives of the Prophet (pbuh) should be avoided. The Prophet’s (pbuh) wives are all respectable; anyone who insults any of them has insulted the Prophet. I resolutely declare this offensive. The commander of the Faithful, Imam Ali (pbuh) treated her eminence Aisha in such a respectful manner. He treated a woman, who had come to fight against him, with the utmost respect because she was the Prophet’s wife; otherwise the Commander of the Faithful (as) would not stand on a ceremony with anyone: hence, no such disrespect should ever occur.”
(Source)
So, although it is difficult to answer how commonly the Shi'a Muslims disrespect the companions and wives of the Prophet (s) in practice, at least the two most widely followed and most reliable scholars of religious law have issued statements severely condemning this practice. It seems that if a Shi'a curses the sahaba, this behaviour should be attributed to his own self or his culture, rather than part of acceptable Shi'a conduct sanctioned by the highest authorities. In fact, such cursing can be seen as contrary to the laws of Shi'a Islam.
