In my place I'm seeing communal polarisation increasing. Or it is becoming more evident. How would one oppose that in a populace where religion and caste hold good sway, without the opposition giving it more power accidently?

That is a very difficult question to answer! You may already know better than I do, being embedded in your local context. But I can suggest some things to consider.

The first is that religion is not a simple good or bad thing when it comes to organizing. It is another consciousness that can compete with or work with a liberation project. It will depend on its structure, how it exerts powers and who it antagonizes vs. helps. There are two big negative forms of political religiosity that are dangerous to liberation. The first is the obvious reactionary conflation of religion with tradition and factionalization, where it is used as a way to create a societal rift and oppression on the basis of religion. This is largely a distraction from the material basis of oppression, but is it very effective and harmful. The second is when religion is used to "check out" of struggle. For example, I know a local religious leader that tells people that it's okay that so many children are killed by Israelis in Palestine because they are martyred in heaven, the only thing that really matters. While this soothes some of the pain, it can also lead to a form of material apathy and turning away from action. With that said, there are also things like liberation theology and working with religious groups towards liberatory ends. It's something that has to be navigated on a case-by-case basis. It is not wrong to, for example, adopt the position that X group is copptonf Y religion and that this should be rejected, even if you do not personally subscribe to religion Y in the first place. You will be more powerful if you (as in, any organization you may be in) find a group that focuses on religion Y from an angle that is compatible with yours and for you to keep each other safe and strong.

Regarding caste, does this mean you are in South Asia or otherwise interacting with th concept of caste as derived from it? This is also a very challenging thing to consider and there are very good points to be made for addressing caste first vs. class first and how they overlap and are different. If you are in India, I would focus on how you might oppose Hindutva from an angle that is caste-critical and whether there are people in your area that are interested in opposing both. People who have been assigned a lower caste will be more likely to see the injustice and be able to act in their own favor and build momentum, though you can also find and make good use of "caste traitors".

Anyways your question is really about communal polarization. This is not something you can simply prevent as its own quantity. What you can do is build towards the better factions within that community and push your own projects. Our enemies create this polarization, they create and maintain fascists and the false consciousnesses that divide us against ourselves. We can't create unity that centers those false consciousness, is what I'll suggest. Class consciousness is at least a correct consciousness that opposes this division and if you include the additional valid liberation struggles you'll be able to build from firm ground.

I should say that this is not the kind of thing anyone can do alone. All of this would only be realistic to discuss as part of an organization to which you would be contributing your efforts and knowledge. So my real advice is to see if you can identify an anti-capitalist group in your community that seems at least 70% good and see if you can join it. And please do so as safely and securely as possible (in-person communication is best, do not use Whatsapp or Facebook etc).

I've seen leftist n leftish organisations being affected by this.

Lefty orgs are basically always in some form of drama or crisis, so this isn't necessarily an odd thing, haha. I can't give a useful opinion without knowing more about how they've been affected, though.