#109 has clarified the role of PKG_CONFIG_ALLOW_CROSS=1 and made it clear that one actually has to:
Install a sysroot for the target platform and configure it via PKG_CONFIG_SYSROOT_DIR and PKG_CONFIG_PATH, or install a cross-compiling wrapper for pkg-config and set it via PKG_CONFIG environment variable.
It would be really great to offer two actual examples of doing these things, because they look far from trivial. I think it would suffice to pick one common combination like building on x86_64 with a target of armv7 involving e.g. libasound2, similar to this example for cross-rs.