Does NFC work without a SIM or mobile data?

Two unrelated things

A SIM identifies a phone to a mobile network. NFC is a radio exchange over a few centimetres between a phone and an object in front of it.

They share nothing. A phone with no SIM, no data plan and no coverage reads tags exactly as well as one with all three.

An old phone kept as a reading device, with no SIM in it, is a perfectly good tool and a common one on a production bench.

What actually needs data

The destination, when the tag holds a web address. The tag delivers the address, the phone tries to open it, and that step needs a network.

So a tap on a phone with no data produces a browser that cannot load, which people report as the tag not working.

Content stored on the tag itself needs nothing. Text is displayed, a contact is offered, a phone number is dialled if there is service to dial with.

That distinction between the tag delivering and the phone acting is the whole answer, and it applies to coverage generally rather than to SIMs specifically.

Where this is useful

A dedicated reading phone with no SIM, kept on a bench for writing and verifying. Cheap, unsubscribed and entirely capable.

Deployments in places with no coverage, where the content has to be on the tag and the absence of a SIM is beside the point.

Devices for children or staff without a mobile subscription, which can still use tags for anything held locally.

And testing, where removing the SIM is a quick way to reproduce what a visitor with no signal will experience.

Payment is different again

Paying with a phone uses card emulation rather than tag reading, and it involves credentials issued by a bank.

Whether that works without data depends on the credential and the issuer rather than on NFC, and it is a different question with a different answer.

So do not reason from one to the other. A phone that pays without a signal tells you nothing about whether it will read a tag, and the reverse holds too.