Our response is crucial, and our first response might actually say more about us than we imagine.
Okay, you might not think in terms of dishonouring God, but I'd hazard a guess that there would be all sorts of questions that might have more to do with missing an opportunity to preach the gospel or something similar. I have them too. But I'm also drawn to wonder what role I might play by getting alongside a family and simply serving them as best I can in a way that meets their needs at that time rather than fulfilling some theological criteria.
And it's not just a theoretical question. While I haven't yet been asked to do a non-religious funeral, I have been asked if I'd be prepared to do one. And that in itself makes me wonder what I might do and how I might do it. It seems to me that while the family might not want anything religious that doesn't mean I can't prepare prayerfully, serve prayerfully and support them in prayer, even if they don't know it! I don't stop being a disciple of Jesus Christ just because I'm in a non-religious setting, doing non-religious things.
In the end, non-religious might simply mean not having someone in a cassock with a dog-collar on. I've done plenty of funerals where the family have said to me, "He wasn't very religious you know. He didn't go to church, but he did say his prayers every night."
It's not for me to judge, I'm there to serve. All people matter to God. It's a phrase I learnt from Willow Creek and it's a phrase that shapes much of what I do and think. All people matter to God, and therefore all people should matter to me.
Perhaps a final word from Paul might focus my thoughts:
Whatever you do, work at it with all your heart, as working for the Lord, not for human masters,