Tasawwuf does not promote celibacy. Marriage is highly encouraged by all paths of Tasawwuf as the teachings are based on Quran and the Sunnah of the Prophet ﷺ. Sexuality is not considered inherently evil as it may be considered in some other religious denominations. Practicing sexuality is permissible as long as its being done in accordance to Islamic teachings. Almost majority of great Imams of Sufis were all married and had children.
One of the Prophet's companion named Uthman bin Mazoon decided to worship every night, all night without sleeping and fasting every day without break which caused his wife to complain to the Prophet ﷺ. The Prophet ﷺ told Uthman “Uthman, am I not the one you should follow?” Uthman wondered what the Prophet ﷺ was alluding to, and when the Prophet mentioned his night worship and fasting, Uthman confirmed that he did. The Prophet said: “Do not do so. Your eyes have a claim on you; your body has a claim on you; your family has a claim on you. You may worship a little and go to sleep; and you may fast some days, but not every day.” Uthman then acted on the Prophet’s advice.
In reality there has been very few Sufi Tariqahs (paths) within the Sufi tradition of Islam who accepted the practice of celibacy and this is due to contradiction of what Islam teaches and what is called Monasticism. Allah ﷻ says in the Quran: (Al Quran 57:27) "...But monasticism was something they invented- We did not ordain it for them- only to seek God’s pleasure, and even so, they did not observe it properly." This was revealed in reference to early history of Christianity where monks lived a reclusive life complete devoid of any pleasures at all, including celibacy practice as a way to imitate Jesus son of Mary (alaihi salaam). This tradition however did not last long among them as the instincts placed by Allah ﷻ within human nature conflicts with this complete reclusive lifestyle that a human tries to adopt.
A sufi who practiced celibacy had a dream related by Imam Ghazzali (r.a), himself a medieval Sufi Imam and theologian, in his well known book called Ihya: The sufi saw himself in dream that it was a day of judgment and all men around him were being fed and given fresh water by these children, however he noticed that none of the children catered him to which he inquired to one of the angels as to why he wasn’t being looked after by these children while all other men were being take care of. The angel answered that all these men were their fathers and since he didn’t have any children he wasn’t being looked after. The moment he woke up he immediately decided to get married. Prophet Muhammad ﷺ said: "all deeds of the dead cease to benefit them from this world except for 3 and they are continuing charity, knowledge that others benefit from, and a righteous child who prays for him." (hadith)
Concept of Zuhd (Renunciation)
However there is a concept within Sufic tradition referred to as Zuhd (Renunciation). This means renunciation of the pleasures of the world by not actively seeking them and be satisfied with what Allah ﷻ gives one and be patient with what Allah ﷻ deprives one. This does not mean complete renunciation of all and everything.
The Persian Sufi Imam Al-Qushayri mentions in his Risala what generally sufis have described about this practice “Zuhd (renunciation) of that which is prohibited is an obligation, whereas renouncing that which is lawful is a virtue. They also say that having little property – provided that the servant of God endures his condition patiently, satisfied with whatever God has apportioned for him and content with what God bestows upon him – is better than living comfortably and lavishly in this world, for God Most High urged His creatures to abstain from this world, when He said: “The enjoyment of this world is little; the world to come is better for him who fears God.” (Al-Quran 4:77). There are many other verses [in the Quran] that disparage this world and enjoin men to renounce it. Waki bin. al-Jarrah, who wrote a Kitab Al Zuhd (Book of Renunciation) said: “Renunciation of this world means cutting short one’s hopes rather than eating coarse food or wearing a woolen cloak.”
Sufis who practiced Zuhd extensively to the point that they lived their lives without marrying were Ibrahim Bin Adham, Rabia Basri, a famous female Sufi saint from Basra, Iraq and even the famous Sufi of Baghdad Abdul Qadir Gilani (r.a) did not marry till in his 50s. However one thing to mention here is that such Sufis never imposed restrictions on their followers, they imposed such restrictions only on themselves because they realized their own spiritual status. For instance the great Sufi Sahl Tustari used to fast for 7 days, going without food and water. His followers tried to imitate him but he informed them not to do so because Allah ﷻ was providing him Rizq (provision) from other sources (spiritually), therefore they had not reached that level yet. Therefore the celibacy is considered a blessing if they are unable able to marry due to financial conditions or other circumstances brought about by Allah ﷻ, as the sufis say ‘Allah deprives only His chosen ones from this Duniya (world and its pleasures).’ but they don’t prefer to make this a condition for this path because if they did then they would be contradicting Shariah (Islamic Law) and Shariah is absolutely necessary for the majority who travel this path.