As per the Pancharatra Agamas which are followed by the Sri Vaishnava community, there is no restriction for followers and learners based on varna. Shudras even serve as priests in the Vaishnava temples.
That is not true in the slightest, and I'm sorry that I gave you any impression to the contrary in my question. That was written in the early days of the site, back when I didn't know as much. Low-caste people are definitely not allowed to be priests in Pancharatra temple (or, for the record, in Vaikhanasa temples). And there are caste restrictions mentioned in the Pancharatra Agamas. Here is what page 242 of this book says concerning the Satvata Samhita:
[T]he [Satvata Samhita] allows only the Brahmana initiate to worship the Vyuha gods with their Mantras. Others (Kshatriyas, Vaishyas, Shudras) are not initiated in the Vyuha mantras. But, if they are totally self-surrendering devotees, they may worship the Vyuha gods without their Mantras.
What is true, though, is that the Pancharatra Agamas do not have caste restrictions on studying them. (Just like Puranas, Itihasas, etc. don't have caste restrictions.) But they do not contradict the notion that the Vedas have caste restrictions.
On the other hand, Sankaracharya considered Pancharatra Agamas as non-Vedic in nature.
Yes, Adi Shankaracharya thought that the Pancharatra Agamas contradicted the Vedas, because he interpreted them as saying that the Jivatma originates from Brahman. But Yamunacharya's Agama Pramanya and Ramanujacharya's Sri Bhashya present detailed arguments to show that properly interpreted, the Pancharatra Agamas do not actually say the Jivatma originates from Brahman. Most commentators on the Brahma Sutras agree with Yamunacharya and Ramanujacharya, and even some Advaitins agree as well. See Vedottama Bhattaraka's Tantra Shuddha, for instance.
EDIT: You asked one more question:
Vedanta sutras do not allow Shudras to study Vedanta but Vaishnava samskara is irrespective of Shudra or not. Why is it so?
Because you are comparing apples and oranges. Adhyaya 1 Pada 3 of the Brahma Sutras says says that low-caste people are ineligible for Upanayana, and are thus ineligible for Vedic study. But that does not mean they are ineligible for all kinds of Diksha, or that they are ineligible to study all kinds of texts. Low-caste people are eligible to learn Agamas, Puranas, Itihasas, etc.