What replaces SD card in industrial applications
SD cards are common in industrial applications.
There are industrial-grade SD cards. Quick search reveals that most of them are rated for operation -40°C to +85°C, eg. Amtron.
When it comes to vibrations, there are vibration-resistant slots, like this one designed for automotive. Many (arguably most) SD slots are spring-locked, thus already resistant to vibration. That's because even for consumer devices vibration cannot be ruled out.
So unless your particular scenario presents unique challenges, SD card will work.