If you're predisposed to believing that retailers are in league with national security agencies and the Federal Government has nothing better to do than to track you buying toilet paper at Walgreens then nothing that we can say will convince you otherwise.
NFC itself has been around since 2004, I've had and used it since 2012. It's not new.
It's a multimodal communication system for very short range.
http://electronics.howstuffworks.com/near-field-communication.htm
If you don't like it, don't use it, along with not using Bluetooth, wifi and mobile data, all of which fall into the same category - the only differences being frequency, power, range, ease of use, and security models.
And funky said nothing about sending data to their website. He said "taken to their website" and no, it's not a big deal.
I was eating lunch with my sister recently - she picked up the ketchup bottle, pointed to a funny square pattern and asked me what that was.
I pointed my cell phone camera at it, used my QR code scanner, and was taken to the ketchup website (Hunt's or Heinz, I forgot) and we had a good time reading about the history of ketchup.
At no time did the ketchup bottle capture information and transmit it to the evil overlords.
An NFC tag is the same exact thing but it uses radio instead of light and a camera.
The reason that the antenna is sometimes a sticker on a battery is because it's cheaper to make that way. It's a loop of wire, not a heavy duty antenna like the others in your phone.