Jai Shri Krishna,
In the Shrimad Bhagavat, Shri Shankar Bhagavan has been referred to as 'Vaishnavaanaam yathaa Shambhuhu', meaning, Shri Ved Vyas ji has described Lord Shankar Bhagavan as a Vaishnav. This is perfectly true because our Bhole Baba is the leader of the path to devotion (bhakti).
Remember, Shri Ram katha was first and foremost narrated by Shri Shankar Bhagavan. It is in the nature of a true devotee to keep chanting their beloved deity's name day and night. In Baalkaand (the first chapter of Shri Ram Charit Manas) Shri Tulsidasji describes the following chopaay (verse) on how Shri Bhole Baba continuously recites Shri Ramji's name:
'Tum puni Ram Ram din raati, saadar japahu anang aaraati.'
Shri Tulsidasji created Shri Ram Charit Manas with the inspiration of Shri Bhole Baba which is why he offered this divine scripture to Shri Shankar Bhagavan.
There is a well known katha that when Shri Goswami Tulsidasji wrote Shri Ram Charit Manas the Sanskrit scholars refused to approve and respect the Manas as a scripture as it was written in Hindi instead of Sanskrit. In the end, it was decided to leave all the scriptures in Baba Vishwanath's temple, where Shri Ram Charit Manas written by Tulsidasji was kept at the bottom of the pile and the doors to the temple closed.
It has been said that the next morning when the doors to the temple were opened, people were surprised to see that Shri Ram Charit Manas written by Tulsidasji was now on top of the pile of all the scriptures and Shri Shankar Bhagavan had written three words on top of Shri Ram Charit Manas: 'Satyam Shivam Sundaram'.
Since Lord Shiv respected and approved Shri Ram Charit Manas, this scripture, even to this date, leads us towards our welfare and towards Lord Shiv.
Jai Bholenath to all the devotees on this very auspicious occasion of MahaShivratri.