A small compilation based on stories I've heard from Ingush people:

1. It's not customary here for a man to communicate directly with his father-in-law and mother-in-law. He definitely helps them, but only through his wife.

2. Polygamy is rare, but it happens. And everyone's fine with it.

3. Three kids in a family is considered small. Five or six is just right. But there are plenty of families with even more. It's no wonder this is the second-fastest growing republic in Russia.

4. Everyone knows their family history going back 10+ generations. And they maintain connections with members of their clan. And absolutely no marriages within the teip. Even though the largest teips can have over 20,000 people (!). Even if a guy and girl are related in the tenth generation back. Mixed marriages with other nationalities are very much frowned upon (though there are more exceptions nowadays).

5. Ancestral towers still hold huge significance. The teip tries to restore them whenever possible. But restoration is an extremely expensive and labor-intensive process. Because most of these complexes are of federal importance, and the government requires tons of project documentation and detailed work plans. Bureaucracy makes up more than half the restoration costs.

6. The Ingush are deeply religious and view Islam as a blessing that saved them from blood feuds and other savagery of traditional beliefs.

7. People are concerned about Ingush territories that ended up in neighboring republics. And they clearly don't like their neighbors for that.

City folks might be less conservative, but in rural areas, that's how it is.