Do I need to re-calibrate my load cell anytime I remove it then remount it on my machine?
Under general circumstances, re-calibration may not be required but there can be exceptions.
It’s also a question of risk and how much risk someone wishes to accept.
Some industry quality standards (ASTM E4, ISO 7500-1) can be interpreted as such and thus re-calibration is required, or additional quality checks for compliance.
The concern is any change in mechanical fixturing, orientation or alignment may affect the performance of the transducer.
Ultimately, it’s up to the user per their own internal quality requirements or in some circumstances they may be required for compliance with an industry quality standard.
In summary, there is no blanket yes or no rule for everyone. It depends upon the situation and the level of risk someone may choose to accept.