Religion
Although Azerbaijan is nominally a totally secular state and has a majority of agnostics and non-religious people, 95 percent of the population is Shiite Muslim. This holds true not just in big cities but also in small towns and rural places.
Never presume that someone you do not know is religiously fervent in Islam or any other faith, or that they have a belief in God. Investigations into people's religions are generally undesirable, and public demonstrations of your faith outside of places of worship ought to be kept to yourself.
Saying grace, for instance, is probably going to be regarded with confusion and quiet. While acceptable, wearing religious clothing like Muslim head coverings, kippahs, or even t-shirts with religious slogans will make many Azerbaijanis uneasy. Authorities can be suspicious of those with long beards. If you respect it, others will respect you as well.