Programming skills, or at the very least scripting skills, are needed for the most visible of contribute-upstream roles in these projects. A lot of work goes into making things like startup run faster or more efficiently, and that requires no little bash-scripting to make happen.
One area where sysadminly skills do come in handy is in support forums. Get good at these areas and start helping other people. This is contributing to the community, it may not feel like it, but it does make the entire ecosystem nicer to live in.
Another area is to participate in testing development builds. This will require some hardware or at least VM space, but provides very needed feedback to development about what's working, what's not working, and provides you a lot of troubleshooting experience. That kind of troubleshooting is a great way to get to know your project better. Do it long enough and you'll get your skills honed enough to start contributing patches to fix problems, or maybe even pick up a somewhat rare but very useful (to the community) skill like manual RPM packaging.