Solution
This is an expected behaviour as builts are different,
The inconsistency happens because you are relying on implicit string/hex display behavior and different implementations, so x86 and x64 end up hashing or formatting different underlying byte data even though it looks the same visually.
You can make the below modification to the LabVIEW code to resolve the issue, where the output string is designed to explicitly converts the string into a HEX string.

Note: The Output indicator should be set to "Normal Display" as the conversion of Hex has been explicitly performed.
As a result you will be seeing the expected outcome in both the executables matching the online tool results as shown below:
SHA253 - Online tool:

x64 Executable:

x86 Executable:
