Like Brian, I've seen 13.56-MHz contactless smartcard readers, as well as 125-kHz proximity readers, installed successfully in high RF environments, such as television and radio transmission stations.
Two points to consider for every install:
First, use cabling between the card reader and electronic access control panel with an overall metal foil shield.
Second, using the cable’s drain wire, connect the cable's metal foil shield to earth ground.
The drain wire carries noise currents, commonly induced onto the cable's metal foil shield by electromagnetic interference or EMI, to earth ground. Earth grounding is essential in preserving the signals carried by the individual conductors protected inside the cable’s metal foil shield, allowing the electronic access system, including the card readers, to function as intended.
Here's a link to a short, informative article on grounding that might be found useful: https://www.securitysales.com/integration/making-sure-your-installations-are-firmly-grounded/.