Writing anything in C is a bad idea these days, and requires active justification that only applies in some situations. Essentially, almost no new projects should be done in C.

Re-doing your build system, or writing a build system for a new project, counts as something new, so should probably not be done in C.

In general, I don't think your build (or build system) should necessarily be specified in the same language as most of the rest of your system.

However I can see that if most of your system is written in language X, then you are pretty much guaranteed to have people who are good at X amongst your developers, so there's some natural incentive to use X for the tooling, too.

In any case, I would mostly just advice against coding anything complicated in shell scripts, and to stay away from Make and autotools, too.

There are lots of modern build systems like Shake, Ninja, Bazel, etc that you can pick from. They are all have their pros and cons, just like the different distributed version control systems have their pros and cons; but they are better than autotools and bash and Make, just like almost any distributed version control is better than CVS and SVN etc.