The story is much more enlightening, and frankly, more educational than this meme projects. Yes, it's correct, at least on a surface level, but there's also the reason they decided to create a secular state. Namely, even though they were all, broadly speaking, Christians or Christian-inspired deists, they also recognised that Christianity came in hundreds of different flavours, not all of which are agreeable. They recognised that a religious state would have to pick a side in all of the hundreds of different spats that Christians have gone through over the most minute details of their dogma. Furthermore, they also realised that a state is most fragile when it is just founded, and thus, to survive, the state would have to have as much support as possible. Pretty much everyone was at least begrudgingly satisfied with a secular state.

You see, if they had created a religious country, they could not guarantee that it would stay loyal to whatever interpretation they had settled on. Future governments could, if they were able to, could easily "reinterpret" the state dogma to whatever they wanted. They understood that if the Government had the power to meddle in religious affairs, it was only a matter of time before someone whose religion was not agreeable to take over and start doing things that you don't like, justifying it with their religion.