Why should a law in a secular state differ based on religion. When you focus on exclusions or differences which affect laws of the country it simply means that you are above the constitution.
I agree it should not. But that goes back to the definition of a secular state. Secular can mean either of two things:
1. No preference for any religion
2. Equal preference for all religions.
India never defined what kind of secularism it wants. That is why we have this conundrum. Usually (and by your own verbiage) Muslims are being asked to give up their "laws", but the same is not expected or even demanded for other communities.
If India were to firmly move towards the system of "no preference for any religion", then I don't think you will have many objections from Muslims. However, you know that the Hindus would never entertain this thought, because for them, the Hinduization of society is a stated goal. The UCC is just being used as a cover where Hindu personal laws and privileges will be maintained and Muslims will be targeted as evidenced.
I currently live in a secular country, where I personally have no issue with the secular laws. Precisely because the state does not interfere in the personal religious practices. In matters where Muslim religious rulings are important, there are legal options available. For example, you can follow the Muslim rulings on inheritance by simply crafting a will by an attorney. Absence of a will, means that the state will dispose of your inheritance per the secular laws of the country. The same situation can exist in India as well, if the government chooses to scrap the Muslim Personal Law.
The same can be said for polygamy as well. Personally, no one I know has ever practiced this, so it is really a non-issue for me and most Muslims. Should the government choose to scrap this provision, what will happen is what is practiced among the Hindus - that is - the start of the "rakhel" system, where a man has a wife and maintains a mistress on the side.
The points you raise are typical dog whistles that are prevalent among Sanghi circles but rarely even discussed among Muslims, mostly because they do not exist within their society.