If you're seeing good support for musl, I'd be interested in receiving a patch to add it as another combination. I prefer to keep the libc apart from the kernel (the mistake we made long ago was to mix them) so that we don't have issues anymore when building on other libcs. For example getaddrinfo tends to be bogus on uClibc and must not be enabled there. And threads do not work on dietlibc if I remember well.
I haven't used HAProxy in any environments other than testing, but as far as I can tell both variants behave equally. In fact, haproxy.cfg for both images is the same, they only differ in their build flags.
Oh yes absolutely! For example last time I checked libmusl, you didn't need -lrt, -ldl, -lcrypt nor a few others which I forgot about. It just provides empty stubs for those so that you can use the same build options as you regularly use with glibc. However for me threads were not supported (it was on a MIPS, lacking some 64-bit atomic ops haproxy relies on). So I'd be tempted to suggest having less options by default with musl since it's mostly aimed at embedded systems, and leaving it to users to choose if they want to enable more or not.
Correction: this requires to add -latomic there (just tested). I should mention this in the INSTALL file.