Hindu scriptures clearly prohibit a Shudra from studying the Vedas. Let us see the commentary on Brahmasutra 1/3/38
And on account of the prohibition, in Smriti, of (the Sûdras’) hearing and studying (the Veda) and (knowing and performing) (Vedic) matters.
Adi, Shankaracharya commenting on it writes,
“The Sûdras are not qualified for that reason also that Smriti prohibits their hearing the Veda, their studying the Veda, and their understanding and performing Vedic matters. The prohibition of hearing the Veda is conveyed by the following passages:
‘The ears of him who hears the Veda are to be filled with (molten) lead and lac,’ and ‘For a Sûdra is (like) a cemetery, therefore (the Veda) is not to be read in the vicinity of a Sûdra.’ From this latter passage the prohibition of studying the Veda results at once; for how should he study Scripture in whose vicinity it is not even to be read?
There is, moreover, an express prohibition (of the Sûdras studying the Veda). ‘His tongue is to be slit if he pronounces it;his body is to be cut through if he preserves it.’ The prohibitions of hearing and studying the Veda already imply the prohibition of the knowledge and performance of Vedic matters; there are, however, express prohibitions also, such as ‘he is not to impart knowledge to the Sûdra,’ and ‘to the twice-born belong study, sacrifice, and the bestowal of gifts.’–From those Sûdras, however, who, like Vidura and ‘the religious hunter,’ acquire knowledge in consequence of the after effects of former deeds, the fruit of their knowledge cannot be with held, since knowledge in all cases brings about its fruit.
Smriti, moreover,declares that all the four castes are qualified for acquiring the knowledge of the itihâsas and purânas; compare the passage, ‘He is to teach the four castes’ (Mahâbh.).– It remains, however, a settled point that they do not possess any such qualification with regard to the Veda.”
Acharya Ramanuja commenting on the same Brahmasutra writes,
“The Sûdra is specially forbidden to hear and study the Veda and to perform the things enjoined in it. ‘For a Sûdra is like a cemetery, therefore the Veda must not be read in the vicinity of a Sûdra;
”Therefore the Sûdra is like a beast, unfit for sacrifices.’ And he who does not hear the Veda recited cannot learn it so as to understand and perform what the Veda enjoins. The prohibition of hearing thus implies the prohibition of understanding and whatever depend son it.”
So, here we have two of the most influential Hindu schholars and intellectual giants totally prohibiting the Shudras from studying the Vedas..
Interesting, u conveniently forgot Rishi Dayanand and Arya Samaj . Arya Samaj allows shudras to study the vedas and become brahmins. Thus, your half-truths are exposed.
AUM says:- “As I have given this Word (i.e., the four Vedas) which is the word of salvation for all making [Here some one might say that by the word Jana, which we have translated into all mankind, only Dwijas are meant, as in the Smritis ( so-called) they alone are allowed to study the Veda but not women and Shoodraas, the other half of this verse answers this objection by adding] – Braahmans, Kshatryas, Vaishyaas, Shoodraas, women, servants, aye, even the lowest of the low, so should you all do, i.e., teach and preach the Veda and thereby acquire true knowledge, practise virtue, shun vice, and consequently being freed from all sorrow and pain, enjoy true happiness.” YAJUR VEDA 26:2.