This dual citizenship thing is BS.
I like the Indian way.
You are either Indian or you are not.
That may sound 'catchy' but it does not help the discussion.
What is a 'citizen' ? A 'citizenship' is an ideological and political statement. It basically says I am at least alleged to have loyalty towards a politically recognized entity. So as an American, I am at least alleged to have my loyalty towards the US. It does not matter if I am US born or not. A 'citizenship' is a status that is independent of race or any other forms of origins.
That does not mean race and/or origins cannot be determining and/or criterion towards the grant of citizenship, whether that grant is somehow automatic (birth) or conditional (immigration).
So...
You are either Indian or you are not... means what ?
What is the main determination factor ? Is it birth inside the borders of a political entity call 'India' ? Is it skin color, implying race ? Is it from name implying proof of lineage ? What ?
A citizenship does not automatically mean the grantor of citizenship -- country -- automatically lose the person if he/she decides to apply his/her loyalty towards another country, whether he/she decides to officially become a citizen of that other country. If India have automatic grant of citizenship via birth, then in order to clear up any confusion, India must make it clear that if a person chose to pledge allegiance to the US, that person automatically loses his/her Indian citizenship. In this case, a person cannot have dual citizenship between India and the US. India can further clear it up by saying there is no need for official renunciation of Indian citizenship at the moment of pledge of allegiance to the US, and that a verbal pledge as witnessed by others, some forms of documentation, or even merely visiting the US by physically being in the US, is enough for an automatic loss of Indian citizenship. But if India -- or any country for this matter -- says nothing about a loss of citizenship and how such a loss can be incurred, then we now have this discussion.
Here is the US oath of naturalization:
Naturalization Oath of Allegiance to the United States of America | USCIS
"I hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty, of whom or which I have heretofore been a subject or citizen; that I will support and defend the Constitution and laws of the United States of America against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I will bear arms on behalf of the United States when required by the law; that I will perform noncombatant service in the Armed Forces of the United States when required by the law; that I will perform work of national importance under civilian direction when required by the law; and that I take this obligation freely, without any mental reservation or purpose of evasion; so help me God."
Note the highlighted. The oath does not demand that I officially renounce citizenship to my previous country. It only demands that I renounce 'allegiance and fidelity', which are moral, not political, precepts. The US requires that I verbally and publicly pledges allegiance and loyalty to the US and that is sufficient for the US to grant me citizenship. The US can also say that I have to live in the US for X yrs, paid the legally required taxes, have no felony convictions, be right handed, speaks with a Texas accent, and so on.
What if the US also demand that I provide proof of official renunciation of my previous citizenship but that my country of origin refuses to allow me to renounce that citizenship ? What if India does that to all Indians who currently holds Indian citizenship -- do not allow the official renunciation of Indian citizenship ?
That is why the US simply ask that you pledge allegiance, live in the US for X yrs, have no felony convictions, be right handed, drives only American branded cars, eat one burger from either MacDonald's or Burger King a day, etc...etc...in order for you to become a US citizen. You can meet all the other conditions but lie about your allegiance for all we care. We just want your public and verbal expression of that pledge. You can become a US citizen and spy for the country of your true and hidden allegiance -- if you want. If you are a non-US citizen and got caught spying, then you just go to jail for a long time. But if you are a US citizen and got caught spying for another country, whether you have any moral allegiance to that country or not, then the brand 'traitor' will be applied and you could be shot for treason. That verbal and public pledge carries moral consequences as well as benefits, tangible and else.
There are plenty of people at all strata of US society that carries dual citizenship. But people generally confuses citizenship with allegiance.