I'm assuming that by "shell" you are referring to the particular shell that you use as the login shell of your Unix system.
Software on your machine may well depend on a particular shell, but it will not depend on the shell that you use as your personal login shell (i.e. it will not depend on the login shell just because it's your login shell).
A utility that happens to be implemented as a script (or partly as a script) may use e.g.
/bin/sh or some other shell to do certain things, but it would work exactly the same way if your login shell was
yash, or some more esoteric shell, just like a Python script would work the same for everyone regardless of what shell they use.
Remember that Unix is a multi-user operating system, and as such, command line utilities as well as graphical applications, would work the same regardless of what command line shell any one user uses (the "plumbing", i.e. syntax for launching the utility, may differ slightly, but it would be consistent within any user's shell).
For an example of a utility that uses a shell script, see e.g. the
firefox executable on some systems (this may be a shell script that launches the actual
firefox binary). Some types of compilers, e.g. OpenMPI, are implemented as shell script wrappers around the actual compiler. Again, programs that does this would work the same regardless of what shell the user is using as their login shell.
On the other hand, a shell script written for e.g.
zsh will not work reliably when executed by another shell. This should be no surprise as replacing the interpreter of any script with another one may well break that script (for example, running a Perl script with the Ruby interpreter is likely to fail).