If you're wondering why would I want that - it's for my own security: against identity and data theft.
Yes. Your issuer can disable transactions that are generated by NFC card. For NFC card, the Integrated Circuit Card (ICC) contains an additional secret key which generates cryptogram (Message Authentication Code) over the transaction data. If you ask your issuer to disable NFC transaction, it invalidates this secret key so cryptogram is no longer authorised.
They don't delete this key so that you can request to enable it again. Contactless payment can be still be processed by the terminal but the issuer responds with decline message. Source: My friend did it by contacting his bank and we tested it later. Transaction results in decline.
Regarding personal IDs, it depends on the usecase. For example, my workplace uses NFC smart card to enter into the workroom. To enter into the building, the only way possible is to let the terminal scan my ID card. The ICC is embedded which does actual authentication for NFC. If your organisation supports both physical (as a fallback mechanism) and contactless then yes they can invalidate authentication done by NFC. The only reason why would they do that is if they want to prevent NFC relay attacks on employees who have access to confidential area but want to maintain both mechanisms for the others.
Note that, the issuer can only invalidate transaction generated by NFC card. It cannot disable the NFC chip itself. Unless you tamper with NFC or shield it, NFC card can be used as normal. A fraudulent NFC reader can still read your passive card data.
You cannot disable NFC of ePassport as it is intended to be used that way by the authorities.
If you want your card or IDs not to be read, you need what some people call Faraday cage which they are not. Faraday cage is grounded. The foil that shields the card from NFC reader only reduces the strength of the signal and does not block it. High power crafted NFC readers can still read your card from distance. What you really need is a reflector that bounces back the signal as noise or a jammer which creates its own field to jam the signal.