It's desirable, in fact, to change GNU Make to check a hash of the file contents and only rebuild if the file has actually changed (and ignore the timestamp).
You can hack this into GNU Make using md5sum (I'm assuming you're on a system with Unix-like commands). Here's a little example that builds foo.o from foo.c but only updates foo.o when foo.h has changed... and changed means that its checksum has changed:
to-md5 = $(patsubst %,%.md5,$1)
from-md5 = $(patsubst %.md5,%,$1)
foo.o: $(call to-md5,foo.h)
@$(if $(filter-out $(shell cat $@ 2>/dev/null),
$(shell md5sum $*)),md5sum $* > $@)
This works because when foo.h was mentioned in the prerequisite list of foo.o it was changed to foo.h.md5 by the to-md5 function. So GNU Make sees the prerequisites of foo.o to be foo.c and foo.h.md5.
Then there's a pattern rule to build foo.h.md5 (the %.md5 rule) that will only update the .md5 file if the checksum has changed. Thus if and only if the checksum has changed does the .md5 file get changed and foo.o rebuilt.
The %.md5 rule is forced to run by having a dummy prereq called FORCE so that every MD5 hash is checked for every prerequisite that GNU Make needs to examine.
First the rule uses a filter-out/if combination to check to see if the MD5 hash has changed. If it has then the %.md5 rule will run md5sum $* > $@ (in the example md5sum foo.h > foo.h.md5). This will both update the hash in the file and change the .md5 file's timestamp and force foo.o to build.
If within the rule for foo.o $?, $^ or other automatics that work on the prerequisite list were used these need to be passed through from-md5 to remove the .md5 extension so that the real prerequisite is used in the commands to build foo.o.
In the example this isn't necessary.
If the foo.h.md5 file does not exist then the %.md5 rule will create it and force foo.o to get built.
You can also adapt this tip to work with different definitions of 'changed'. For example, the .md5 file could store the version number of a file from the source control system and rebuilds would only happen when the version had changed.