Good question. In India, caste is not unique to just 'hinduism', it is there among Christians and Muslims. In fact, in many villages, no one asks others 'what religion do you belong to'. The question if ever asked is "what caste one belongs to" In some parts of south India I am familiar with the caste muslims belong to is called "turaka". There is another caste in muslims, they belong to cotton weaving. Tha caste name is "pinjara", etc. Just because pinjara and turaka are muslims, they don't marry across the caste lines. Even among muslims, I heard, sheikhs marry sheikhs, pathans marry pathans, etc. Same thing goes with 'oppressed castes' or Dalits: there are many castes in SC; they don't marry across castes.

Where do you see injustices? Since everyone in (at least rural) India belongs to some caste, does every injustice becomes a "caste injustice"? In south India, Brahmins, Ksatriyas, Vaisyas (the standard Manu story) are not powerful at all. Some castes from Sudras are powerful in some villages; not every caste is powerful across the cross section of India: caste A in village X is powerful; however, the same caste A is super weak in village Y.

The powerful have two characteristics: they have more land or they have more relatives in village who can come to aid you or both. Whenever there is an irresolvable dispute between two parties in villages, this leads to fights. Imagine this dispute between a muslim farmer and a hindu farmer, and this hindu farmer goes and moves the land border by 10% more. Muslim farmer goes to the village elders, who belong to neither one religion nor one caste. Elders also agree that it is "anyaaya" to take that 10% land, however this hindu farmer doesn't listen. What's next? A fight ensues. Is this fight caste fight? Is this fight communal? Do all hindus in the village support this hindu farmer? Definitely not. Do all caste members of this hindu farmer support him? Not at all. In fact, his caste members also say "it is anyaaya".

So, what happens in such cases is: just raw power wins. In some cases, this raw power also helps 'oppressed castes'. I know many cases where "oppressed castes" just use the legal threat to do all kinds of "anyaaya". In one case, they are sending sewage of all their streets to a farmer land. When this farmer complains, these 'oppresed' people threaten with some SC law. Even govt officials can't do anything.

About the system. Any system requires reproduction, continuity, some kind of dynamic. Which social scientist has laid bare of such mechanism of caste system? Let me paste this thought experiment from here[1]:
----------
As an example, consider one of the things that Europe ‘knows’ about India: the Indian caste system. Almost everyone I know has very firm moral opinions on the subject. Many see in it the origin of all kinds of evils in India: from the denial of human rights to oppression; some see in it obstacles to progress and modernization and so on. I suppose we agree that we need to understand a phenomenon before making moral judgments. With this in mind, if you try and find out what this famous caste system is, and why people either attack or defend it, you discover the following: no ancient book exists that tells us what the principles of the caste system are; no Indian can tell you about its structure or its organization; no scientific theory has been developed that explains how or why it continues to exist. Simply put, nobody understands what it is or how it functions. In that case, how can anyone be pro or contra the caste system? If we focus on how people normally describe this system and understand how easy it is to turn such a description upside down, the absurdity of the situation becomes obvious. While emphasizing that I do not attack and much less defend the caste system in what follows, let us look at the existing descriptions and their consequences.

(a) Caste is an antiquated social system that arose in the dim past of India. If this is true, it has survived many challenges – the onslaught of Buddhism and the Bhakti movements, the Islamic and British colonization, Indian independence, world capitalism – and might even survive ‘globalization’. It follows, then, that the caste system is a very stable social organization.

(b) There exists no centralized authority to enforce the caste system across the length and breadth of India. In that case, it is an autonomous and decentralized organization.

(c) All kinds of social and political regulations, whether by the British or by the Indians, have not been able to eradicate this system. If true, it means that the caste system is a self-reproducing social structure.

(d) Caste system exists among the Hindus, the Sikhs, the Jains, the Christians, the Muslims… It has also existed under different environments. This means that this system adapts itself to the environments it finds itself in.

(e) Because new castes have come and gone over the centuries, this system must also be dynamic.

(f) Since caste system is present in different political organizations and survives under different political regimes, it is also neutral with respect to political ideologies.

Even though more can be said, this is enough for us. A simple redescription of what we think we know about the caste system tells us that it is an autonomous, decentralized, stable, adaptive, dynamic, self-reproducing social organization. It is also neutral with respect to political, religious and economic doctrines and environments. If indeed such a system ever existed, would it also not have been the most ideal form of social organization one could ever think of?

[1] https://www.hipkapi.com/2015/10/01/what-can-india-offer/