I don't get how someone achieves reproducibility of builds: what about files metadata like creation/modification timestamps? Do they forge them? Or are these data treated as not important enough (like it 2 files with different metadata but identical contents should have the same checksum when hashed)?
Generally, yes:
https://reproducible-builds.org/docs/timestamps/Since the build is reproducible, it should not matter when it was built. If you want to trace a build back to its source, there are much better ways than a timestamp.
C compilers offer __DATE__ and __TIME__ macros, which expand to string constants that describe the date and time that the preprocessor was invoked. Any code using these would have different strings each time it was built, and would need to be modified. I can't think of a good reason for them to be used in an actual production program, but for whatever reason, they exist.
Toolchains for reproducible software likely let you set these values, or ensure they are 1970-01-01 00:00:00