The tech is not the issue, card vs chip = no difference
There is no security in obfuscation
(Image Source, licence CC-BY-NC 2.5)
Since cards of all sorts are moving towards contact-less RFID technology anyway, there is little difference between using a chip or a card to authenticate your identity, other than that it is much harder to steal the chip, which is an enormous benefit for everyone, citizens, companies and authorities (except identity thieves. Boo. Hoo. Cue the tiny violin quintet).
So if you have a premise of a standardized national identity already, then whether you use RFID chips in a loose card or an embedded chip, does not really matter. The technology is not the issue.
If anything would be an issue it would be the existence of a national identity system, not how it is implemented. But as reality shows us...
A standardized national identity does not equal dystopia
As for people talking about how having a national standardized identity system means instant dystopia and The End of Privacy... I cannot disagree more. In my country Sweden, we have a national identity. The instant you are born, or when you have any kind of permanent residency here, you get a personal identity number.
But the fact that you can use that as a key in a database does not mean that all databases can cross-collate their data. In fact, this was one of the first thing that were banned when Sweden as a pioneering country instituted personal data protection legislation. And then there is the simple fact that company A has no reason to let company B or the authorities rummage around in their business data.
Also thanks to the early vigilance, there is now a well ingrained opposition among the public and the authorities to any and all kind of registration of political sympathies, affiliations, religion, sexual orientation or any other kind of "sensitive personal data".
So curiously enough, after over half a century of having a standardized national personal identity system, Sweden has not fallen into dystopia or a nightmare of personal data harvesting, not any more than anywhere else.
But what if... ?
Yeah, what if? What if your government, or a mega-corp, or a criminal syndicates, or a jilted lover suddenly goes off the deep end and decides to start using your national identity to put two and two together and making your life miserable with that? Then we would be much better off if we never had an identity system, right?
Not really, no. First there is the issue of actually getting databases to play nice together. Once that is up and running, it is not as if you did not have an identity anyway, it is just slightly more fuzzy around the edges. You are not anonymous and you are not safe just because your identity is a little bit obfuscated compared to having a standardized national identity. Because as xkcd teaches us above: there is no security in obfuscation. They will find you anyway.
And if you think that you can do the "I am Spartacus" trick and hide in a sea of John Does... sorry, that only works in movies. If there is any kind of uncertainty about which out of a possible few John Does might be the one they want to make their life miserable for, they will not shrug and go "Oh well... guess we better not do anything then"... they will just do it for all of them instead.
A few technical notes
"A RFID chip can be read by everyone remotely"
No it can not if you make chip standard such that only an valid authentic trigger signal will lead to a response.
"If data is on the chip, all data can be stolen by everyone".
See the point above. The chip can be made such that only the data that the reader is permitted to read is released.
"Yeah but there may be bugs..."
Yes. And? There are as many bugs here as the author wants it to be. This means this thing can be more full of bugs than an ant-hill, or have none at all. The author decides.
"All technology can be hacked"
No, Magical Hollywood Hacking only works as well as the author wants it to work. And the fact that sometimes, some things get hacked in real life does not mean Magical Hollywood Hacking is a reality.
"With a chip you can never be rid of your identity"
See the main post: you cannot get rid of it anyway. And even if you somehow could have shed your identity that makes you a highly suspect character. This is because in a dystopia the mere fact that you have gone off-grid is reason enough to cast suspicion on you according to the — very unethical and twisted — principle of "Only those that have reason to hide will hide".