Of course it isn't logical to accept help from a church agency but not want to have anything to do with the church. But maybe especially people who aren't very familiar with the church might feel that church people would be more critical or judgmental, or would expect inside knowledge or rituals that could feel uncomfortable. Some people also have had traumatic experiences with a particular church, or simply disagree with the kind of religion that focuses more on supernatural thinking.
Despite all that, it's also true that a lot of the volunteer work that needs doing is done by church-related organizations. My experience is that while people are doing that kind of practical work, they're thinking and talking about what needs doing and how to get it done, not about churchy stuff. If a church group was doing something worthwhile in your town and you wanted to help, you wouldn't have a lot to lose by just telling them you were interested in the volunteer work but not in religion per se, and asking up front if it would be okay to help out on that basis. I can't imagine anyone turning you away. You might even meet some other not very religious people doing the same thing.
But at the same time, so many places can use volunteers that you can surely also find a setting that's not church-affiliated, if that's important to you. Every school can use reading tutors, every nursing home can use visitors, every animal shelter can use dog walkers. Even though whatever one person does may only be a drop in the bucket, it's a big step to just pick something and do it anyway. I admire neilo's initiative on that score, as well as his commitment to a healthier lifestyle. neilo, whatever you find, good luck -- I hope your halo will keep on shining. (-: