Fatwa by Shaykh Ibn Baz Fatawa Islamiyah , Darussalam, Vol 4, Page 127
Q. Is it better for the Muhrim to cover the two shoulders or to uncover one of them during the Ihram?
A. The sunnah for the Muhrim is that he places the Rida’ (upper garment) over both of his shoulders and put its ends on his chest. This is the Sunnah and it is what the Prophet (Sallalahu Alahi wa Sallam) did.
So, if the person wants to perform the Tawaf of Arrival (Tawaful-Qudum) , he does Al-Idhtiba’. This is by him placing the center of his Rida’ under his right armpit and its edges over his left shoulder. Thus he uncovers his right shoulder. This is specifically for the Tawaf of Arrival, meaning when the person first arrives in Makkah for Hajj or ‘Umrah.
Then when he completes the Tawaf, he adjusts the Rida’ and places it over both of his shoulders, and he prays two Rak’ahs of Tawaf.
The person who always keeps one shoulder uncovered, this is opposed to the Sunnah, and so is uncovering both of the shoulders. The Sunnah is only to cover both of them with the Rida’ while the person is in Ihram. If the person takes off the Rida’ and does not cover his shoulders while he is sitting or eating or talking with his brothers, there is no harm in that.
However, the Sunnah is that when the person wears the Rida’, it should be over his two shoulders and its ends should be on his chest.