1/3rd of the territory that became Republic of India was princely states like Kashmir with their own sets of laws. They all signed the Treaty of Accession - voluntarily or under duress.
Imagine if different rights existed everywhere from Hyderabad to Bhopal.
Im just telling you what "the fuss" is about...and what the appropriate hypothetical "fuss" would be to compare in other contexts different to India.
People (and their representatives they elect) locally were promised certain things and got used to decades of one system and it was removed overnight after prolonged whittling away. None of which was done with their (promised) consent....and several other injustices done due to the security context which is bigger sordid topic to get into.
US state comparison (that you used) is simply not equivalent to it (for matter of appropriate "fuss" comparison equivalency)....but there are other more relevant things I mention that are somewhat similar in north america....(though the security context is far different....any similarity there was a long time ago in 19th century for the US, though Quebec had a fairly significant 20th century resurgence).
You try change things in Quebec from the federal side or US native reservation operations overnight from DC (after all the norms, conventions and codes established by compromise over long time), you will see similar uproar and fuss then...as now you are comparing something closer to India's case with Kashmir.
To take an extreme (even with a constitutional framework in force for significant part of it)...
The British over a number of centuries cudgeled its neighbouring island in grievous manner (letting some norms wax and others wane at other times, gaslighting plenty on both when convenient for westminster to do so... to have a very inconsistent structure in the end ) that eroded trust and great deal many other things over time.
"The fuss" exploded eventually with Irish liberation and independence (and the pangs still continue with the remnant part in the north and so on).
If India wanted to do its constitution framework and application different from the start, then it should have done so to have more consistent basis on how Kashmir stacks up vis a vis other princely states processes and the regular states (and reorganisation etc).
But thats a deeper thing to get into...how centralised and unified one desires to be in theory versus an often different reality...and how do you shape a republic basic law (i.e the constitution) for it and how it is to be best applied (and knowing hindsight is 20/20) given unification over such a large expanse and population is always going to be a work in progress.
What do you secure, what do you leave flexible given gestation and budding of certain things at an inherited juncture, rather than consolidated trust and maturity.
Same thing goes for having a unified civil code.
There will again be uproar (simple observation without having to take a side on the issue) if its done (esp ad hoc politically) due to leaving it this late after people got used to current norms.
Now if you outnumber "the fuss" by 100 times to 1 (unlike say other ratios like british to irish), you get your way regardless basically.
But its not really a debate or ordered logic (and hard legislative work and application for greater coordination and trust over time) at that point.
Perhaps thats why UCC stalls even with central (and even raw majority desire for it.... political capital and risk is perhaps not worth expending given that the dominant raw ratio isnt there like there was for kashmir's art 370 "abrogation".
