Living in the US for 4 years convinced me that no, the US is not a secular society because religiosity permeates public life. However, European countries by and large don't have separation of Church and State, with most countries having a state-sanctioned church.

The problem of wars of religion was resolved differently on either side of the atlantic centuries ago. On this side, religiosity becomes a private matter which is allowed to coexist with an official church. On the other side, people wear their religion on their sleeve, which is incompatible with the state favouring one religion over the others.

If you are not convinced, try it on someone who has not been entirely debauched by economics. — Piero Sraffa