Shukla Yajurveda 26.2 states:
May I speak the sacred word to the masses of the people (janebhya) (1) to the Brahmana, Kshatriya, to the Shudra and the Arya (2) and to our own men and the strangers (3).
The above verse indicates Vedic mantras can be heard by Shudras.
Now, as some of you know Vedanta Sutras are considered the summary of the teachings of the Mukhya Upanishads which are considered Shruti. So, I expect itself to be a Shruti as well (please feel free to correct me if I'm wrong).
However, the Vedanta Sutras 1.3.38 forbids the Shudras to listen to the Vedas:
And on account of the prohibition, in Smriti, of (the Sûdras') hearing and studying (the Veda) and (knowing and performing) (Vedic) matters.
Adi-Shankaracharya, on this verse, comments:
This is another reason why the Sudra has no right: By the Smriti he is debarred from hearing, studying, and acquiring the meaning of the Vedas. The Smriti mentions that a Sudra has no right to hear the Vedas, no right to study the Vedas, and no right to acquire the meaning of the Vedas (and perform the rites). As for prohibition of hearing, we have the text, "Then should he happen to hear the Vedas, the expiation consists in his ears being filled with lead and lac", and "He who is a Sudra is a walking crematorium. Hence one should not read in the neighbourhood of a Sudra". From this follows the prohibition about study. How can one study the Vedas when they are not to be recited within his hearing? Then there is the chopping off his tongue if he should utter the Vedas and the cutting of his body to pieces if he should commit it to memory. From this it follows by implication that the acquisition of meaning and acting on it are also prohibited, as is stated in, "Vedic knowledge is not to be imparted to a Sudra", and "Study, sacrifice, and distribution of gifts are for the twice born". But from those to whom knowledge dawns as a result of (good) tendencies acquired in the past lives, as for instance to Vidura, Dharmavyadha, and others, the reaping of the result of knowledge cannot be withheld, for the result of knowledge is inevitable. This position is confirmed by the Smriti text, "One should read out to the four castes (keeping the Brahmana in front)", which declares the competence for all the four castes for the acquisition of the anecdotes and mythologies. But the conclusion stands that a Sudra has no right to knowledge through the Vedas.
Why is the Vedanta Sutras contradicting the Vedas?
All right, I found another verse from the Shukla Yajurveda which possibly hints that Shudras can acquire jnana:
O Lord! Provide enlightenment to our Brahmanas, Ksatriyas, Vaisyas and Shudras. Provide me also with the same enlightenment so that I can see the truth. (Shukla Yajurveda 18.48)