Vedantins consider Sanyasa the path of liberation and most of their acharyas have taken up sanyasa in order to attain jnana.
If so then are shudras also allowed to take up sanyasa for the pursuit of moksha?
If yes then which are the vedanta schools/ sects which allow shudras for sanyasa
if no, what are the reasons behind it?
Shudras are not allowed... Whether, even the Kshatriyas or Vaishyas are also allowed, is something that is unclear, if we go by the minor Upanishads called the Sannyasa Upanishads.
The Narada Parivrajaka Upanishad (NPU) and the Brihat Sannyasa Upanishad (BSU), both discuss, the question- Who are all fit to renounce?
From NPU-Chapter3:
Thereupon Narada asked the Grandfather: "Lord, [136] how does a man renounce? And who is entitled to renounce?"
"I shall first explain who is entitled to renounce and then describe the procedure of renunciation. Listen attentively. "The blind, eunuchs, outcastes, cripples, the effeminate, the deaf, the childish, the dumb, heretics, discus-bearers, phallusbearers, Vaikhanasas, Haradvijas,10 mercenary teachers, bald men, and people without a sacred fire: these, even though they are detached, are unfit for renunciation. If they have already renounced, they are not entitled to receive instruction in the Great Sayings.11 An elder renouncer12 is entitled to become a Paramahamsa.
So, Sudras are clearly not allowed, as they don't have the Vedic fire and likewise the Vratyas are also disallowed..
Similarly, from BSU Chapter2:
Sanctified by the forty sacramentary rites, he becomes indifferent toward everything; attains purity of mind; and burns away desire, jealousy, envy, and egotism. [250] Only such a man, endowed with the four aids, is fit to renounce
One should never admit to renunciation apostate renouncers, mortal sinners, Vratyas, and the infamous.3 One should never admit to renunciation those who have neglected vows, sacrifices, austerity, liberality, fire offerings, and Vedic recitation, and those who have fallen from truth and purity.
Now, Sudras do not have all the 40 Samskaras, they are not allowed to recite Vedas either. So, they are clearly not allowed..
Vratyas (i.e who are born in Dvija families but did not receive sacraments within prescribed time) are also similarly not allowed.
Exception - Nothing can prevent a true brahma jnani from renouncing everything (including his body, food to nourish the body, medicine to preserve it, or any relationships arising from the body), irrespective of his varna, if he is simply going to sit under a tree as aja-gara vritthi and let his body drop off like a dried leaf. That means he has reached stage of stitha-pragna, and no rules are going to stop him e.g. Jada Bharatha.
Rule - for normal people, if they live in a society and are a brahma jignasa and want to take up sanyasa for path of liberation, Baudhayana smriti gives the rituals that a brahmachari or gruhastha needs to perform in order to renounce. These are all Veda mantras and rituals, which imply that the doer must be a dvija.
Also, from personal experience, there are complex pre-requisites for sanyasa:
ensure 3 runas (deva,pitru,manushya) are repaid
take permission from one's dharmapatni before renouncing (or permission from mother in case of brahmachari renouncing - you might have heard Adi Shankara story)
extinguish the aupasana agni that they have been kindling since marriage
symbolically perform one's own shraddha ceremony, thereby declaring that they are dead to the world
Detailed rules here - http://www.sacred-texts.com/hin/manu/manu06.htm
Since these rites are only prescribed for those who know Vedas, one can infer that Shudras are not allowed. Nowadays almost nobody does this or wants to, so not much point in talking about who can or cannot renounce.
When Vivekananda took up sanyasa, brahmanas questioned his practice since he was not a dvija. He replied saying that his lineage traced back to Chitragupta (Yama's assistant), and since he is the rule-keeper, he has as much right to renounce as the people whose rules were being overseen. But I'm not aware of any Shastras that explicitly allow it.
According to the Mahabharata, Sudras are not allowed to take up sanyasa.
Once a Sudra enters an ashram containing wide variety of sages. Sudra was well received by persons in the ashram. After observing the ashram, Sudra desires to take the initiation for sanyasa. But Kulapati of the ashram did not agree to initiate him to the path of renunciation saying that Sudras are not allowed to renounce in ashram.
Once upon a time a Sudra endued with compassion for all creatures, ventured to come into that asylum. Arrived at that retreat, he was duly honoured by all the ascetics. Beholding those ascetics of diverse classes that were endued with great energy, that resembled the deities (in purity and power), and that were observing diverse kinds of Diksha, O Bharata, the Sudra became highly pleased at heart. Beholding everything, O chief of Bharata's race, the Sudra felt inclined to devote himself to the practice of penances. Touching the feet of the Kulapati (the head man of the group), O Bharata, he addressed him saying, 1 'Through thy grace, O foremost of regenerate persons, I desire, to learn (and practise) the duties of religion. It behoveth thee, O illustrious one, to discourse to me on those duties and introduce me (by performing the rites of initiation) into a life of Renunciation. I am certainly inferior in colour, O illustrious one, for I am by caste a Sudra, O best of men. I desire to wait upon and serve you here. Be gratified with me that humbly seek thy shelter.'"
"The Kulapati said, 'It is impossible that a Sudra should live here adopting the marks specially intended for those practising lives of Renunciation. If it pleases thee, thou mayest stay here, engaged in waiting upon and serving us. Without doubt, by such service thou shalt attain to many regions of high felicity.'"
Further Bhishma says to Yudhishthira that all other orders are allowed to do take instruction.
Hence, O king, the Brahmana should avoid imparting instructions (to such as are low-born), for it was by imparting instruction to a low-born person a Brahmana came to grief. O best of kings, the Brahmana should never desire to obtain instruction from, or impart instruction to, a person that belongs to the lowest order. Brahmanas and Kshatriyas and Vaisyas, the three orders, are regarded as twice-born. By imparting instruction unto these, a Brahmana does not incur any fault. They, therefore, that are good, should never discourse on any subject, for imparting any instruction, before persons of the inferior order. The course of morality is exceedingly subtile and incapable of being comprehended by persons of uncleansed souls.
गार्हस्थ्यं ब्रह्मदर्यं च वानप्रस्थं त्रयाश्रमाः । क्षत्रियस्यापि कथिता ये चाचारा द्विजस्य हि ।। वैखानसत्वं गार्हस्थ्यमाश्रमद्वितयं विशः । गार्हस्थ्यमुत्तमं त्वेकं शूद्रस्य क्षणदाचर ।। स्वानि वर्णाश्रमोक्तानि धर्माणीह न हापयेत् । यो हापयति तस्यासौ परिकुप्यति भास्करः ।। Transliteration : The 3 âshramas of Brahmacharya, Gârhastya & Vânaprastha are prescribed for the Kshatriyas & the necessary rites described for the Brâhmanas. Gârhastya & Vânaprastha are the 2 âshramas prescribed for the Vaishya. The Shûdra is prescribed only Gârhastya, the best of all.None should give up his dharmas as described by the Varnâshrama system. Bhâskara becomes angry with the man who gives up.[Vamana Purana:15:62-64]
As far as it is known, there are only 2 organisations at present which accept Shudras as Yatis-the Nâgâ Sannyâsins(since they also accept foreigners in their fold) & the Râmakrishna Math and Mission.
There are two ways of being Sanyasi. First is to adapt Sanyasa at early stage of age and another is after completing the 75 years of one's life to enter in Sanyas ashram after the Vanprasth ashram. Shudrs are definitely not allowed to be sanyasi via first way. Though they may become sanyasi by second way (I am not sure though)
