Clearly your use of Abrahamic faiths is not fair in this context when the root of Abrahamic faith is Judaism and it is also an old religion as Hinduism.
Judaism..as it is now.. wasn’t always monotheist. And it evolved over time. And not as old as Hinduism.
Texts and inscriptions and temples from the Vedic period are much older. And that’s why there has been a systematic purge, revisionism, faulty translations and suppression of civilizational history. Hinduism..as it’s known now..is and was decentralized giving it the ability to survive and thrive millennia.
While it can be called many names and has been co opted, our source text is common to all who call themselves Hindu and that is the Vedas…our religious text.
You said: "It worked out well as a diverse society with one identity until monotheistic Abrahamic faiths and their adherents came as invaders and colonizers.".
Abrahamic faiths are monotheistic and against idol worship. While not all Hindus worship idols and multiple gods, these practices are not blasphemy or apostasy.
There is a binary criteria amongst Abrahamic religions about what constitutes membership.
Having said that, they are all covered by the Hindu Personal Law. And there is a separate Muslim Personal Law aka Shariat Law in ‘secular’ India.
For the purposes of the law, they are all Hindus. But from a faith based perspective, they are all separate religions whose congregations are considered a minority.