Contradictory ahadeeth of Infallible Shia Imams, is not a minor issue, that one could just shrug off, comparing it with difference of opinion between Sunni madhabs of jurisprudenc. This matter was so serious that some Shias left Shiism, due to this issue. Which is quite obvious because things such as this are unacceptable from infallibles.
Here are few testimonies from Shia sources showing that how and why some Shias left Shiism.
1. Ahmad ibn Idris from Muhamad ibn ‘Abdul-Jabbar from al-Hassan ibn ‘Ali from Tha’alabah ibn Maymoun from Zurarah ibn A’ayun that he said: I asked Imam al-Baqir (as) a question so the Imam gave me the answer then another man came and asked the same question so the Imam gave him a different answer, then another one came and asked about it so the Imam gave him a completely different answer than both of us. when both men left I asked the Imam: “O son of Rassul Allah, two men from ‘Iraq and from your Shia came to ask you but you gave each of them different answers.” He replied: “O Zurarah, this is good for us so that we may remain safer because if you all agree on this then the people will believe in it and they would be guided to us but we will not remain for long.”
Later I said to his son al-Sadiq (as): “Your Shia always walk away from you with different opinions and answers” so he gave me the same reply as his father.
source: al-Kafi 1/65.
al-Majlisi said: Muwaththaq like the Sahih.
al-Behbudi said: Sahih.
2.
al-Ash`ari al-Qummi says in Firaq al-Shia when discussing the followers of al-Baqir (rah):
[As for those who proved the Imamah for `Ali bin abi Talib, then Hassan, then Hussein, then `Ali bin al-Hussein, and afterwards they declared their belief in the Imamah of his son abu Ja`far Muhammad al-Baqir and remained on this state until his death, except a small group from them, because they heard a man called `Umar bin Rayah claim that he asked abu Ja`far about a matter and he gave him an answer, then he returned the next year and asked about the exact same matter but this time he received an answer that opposes the first answer he originally received. He told abu Ja`far: “This opposes the answer you gave me last year.” he replied: “Maybe our answer was out of Taqiyyah.” so he doubted his Imamah. He later met a man from the companions of abu Ja`far called Muhammad bin Qays, so he told him: “I had asked abu Ja`far about a matter so he answered me, then I asked him about it another year so he answered differently, I asked him why did he do this, he said he did it out of Taqiyyah, and Allah knows that I only asked when I was full of faith in him and sincerity and I wanted to practice upon his verdict, so he had no reason to do Taqiyyah with me.” ibn Qays said: “Maybe he did Taqiyyah because there was someone else in attendance?” He said: “Nobody attended our Majlis in both those times, but his answers were random and he didn’t memorize what he said the previous year so he can answer with it again.” So he disbelieved in his Imamah and said: “He who gives false verdicts cannot be an Imam in any way shape or form, and he who gives his verdicts as Taqiyyah in a way that does not please Allah cannot be an Imam, nor he who sits comfortably at home and keeps his door shut, the Imam must rise against oppression and order what is good and forbid what is evil.” This is why he leaned towards the opinion of the Batriyyah and a small group followed him on this.
sources:
-Bihar al-Anwar by al-Majlisi (73/33) (69/178).
-Tahtheeb al-Maqal fi Tanqeeh Kitab Rijal al-Najashi by Muhammad `Ali Abtahi (3/464
3. The Esteemed Shaykh of Shiism, Tusi says in his Tahtheeb:
ويقول شيخ الطائفة الطوسي في تهذيبه: إن أحاديث أصحابنا فيها من الاختلاف والتباين والمنافاة والتضاد حتى لا يكاد يتفق خبر إلا وبإزائه ما يضاده، ولا يسلم حديث إلا وفي مقابلته ما ينافيه حتي جعل مخالفونا ذلك من أعظم الطعون على مذهبنا وتطرقوا بذلك إلى إبطال معتقدنا، إلى أن قال: أنه بسبب ذلك رجع جماعة عن اعتقاد الحق ومنهم أبوالحسين الهاروني العلوي حيث كان يعتقد الحق ويدين بالإمامة فرجع عنها لما إلتبس عليه الأمر في اختلاف الأحاديث وترك المذهب ودان بغيره لما لم يتبين له وجوه المعاني فيها، وهذا يدل على أنه دخل فيه على غير بصيرة واعتقد المذهب من جهة التقليد
تهديب الأحكام،1/2
And among the Hadiths (narrated) by our companions (Shia scholars/companions of the Imams) are so many disparities, contrast, contravening and contradictions that you will not find a single report that we agree upon which doesn’t have another that contradicts it, and not a single Hadith is safe from another which denies it. These (contradictions) are to such an extent that our opponents (the Muslims/Ahl Al-Sunnah) have used it as the biggest accusation/attack against our school and as a proof for the falsehood of our creed. (Until he said): ‘… and this is why a number (of Shias) have left the true creed and amongst them are the likes of Abu Al-Hassan Al-Harouni Al-Alawi, who used to be on the true creed, upon the creed of Imamah (Imamate), but he turned away from it when confusion overtook him due to the issue of the contradicting Hadiths. So he left the school (of Shiism) and attached himself to another (school), as he could not grasp the different understanding (of our text) and this is an indication that he did not embraced it (Shiism) without insight, rather based on Taqleed. Source: Tahtheeb Al-Ahkam 1/8 by sheikh of the sect al Tusi.
4. Esteemed Shia scholar Ja’far al-Subhani says in “al-Rasael al-Arba’ah” pg.201:
عندما نطالع كتابي: الوسائل، والمستدرك مثلاً؛ نرى أنه ما من باب من أبواب الفقه إلا وفيه اختلاف في رواياته، وهذا مما أدى إلى رجوع بعض ممن استبصروا عن مذهب الإمامية
When we read the two books (of Hadith): Wasael al-Shia and Mustadrak al-Wasael for example, we see that there is NO chapter or Fiqhi section which is free from conflicting narrations, this has caused some of those who converted to the Imami Madhab to leave it.