To be fair, we do usually have an idea of what is meant by 'God'. It's fair to go with the 'usual definition' unless they say otherwise. If they mean God as 'whatever began this iteration of the universe, even if it was a quantum vacuum fluctuation' rather than God as 'supernatural person who created the universe', they should say so because they are using a nonstandard definition. That said, the definition of 'supernatural' is problematic in itself. The real differences I run into when other people use the word 'God' isn't the basic definition, it's all the baggage they tack on in addition, which sometimes seems to be different for every believer.
I'm not anti-Christian. I'm anti-stupid.