Is redo compatible with autoconf?
Yes. You don't have to do anything special, other than the above note about declaring dependencies on config.h, which is no worse than what you would have to do with make.
Is redo compatible with automake?
Hells no. You can thank me later. But see next question.
Is redo compatible with make?
Yes. If you have an existing Makefile (for example, in one of your subprojects), you can just call make from a .do script to build that subproject.
In a file called myproject.stamp.do:
redo-ifchange $(find myproject -name '*.[ch]') make -C myproject all
So, to amend our answer to the previous question, you can use automake-generated Makefiles as part of your redo-based project.
Is redo -j compatible with make -j?
Yes! redo implements the same jobserver protocol as GNU make, which means that redo running under make -j, or make running under redo -j, will do the right thing. Thus, it's safe to mix-and-match redo and make in a recursive build system.
Just make sure you declare your dependencies correctly; redo won't know all the specific dependencies included in your Makefile, and make won't know your redo dependencies, of course.
One way of cheating is to just have your make.do script depend on all the source files of a subproject, like this:
make -C subproject all find subproject -name '*.[ch]' | xargs redo-ifchange
Now if any of the .c or .h files in subproject are changed, your make.do will run, which calls into the subproject to rebuild anything that might be needed. Worst case, if the dependencies are too generous, we end up calling 'make all' more often than necessary. But 'make all' probably runs pretty fast when there's nothing to do, so that's not so bad.