Different cultures have different norms and values, and in some, cousin marriage is more the norm or at least more accepted. Is it weird to date your second cousin once removed? Fuck haters, and please don't be one of them. My second cousin is my parent's first cousin once removed. They do not tell many people their history, but close friends know, it's such an amazing story it just keeps getting out.
In mainstream US culture, you marry strangers, or at least friends of friends or church acquaintances, at any rate, people absolutely unrelated to you.
Can I date my second cousin once removed?
Whether this specific pair should have kids or not probably depends more on their specific risk factors -- it's probably worth going to a genetic counselor if they plan on kids. Is weird that I live with my parents? I think the liberals and conservatives would feel similarly, to be honest. If they share a great-grandparent, they are third cousins. Do they have some issues involving reproduction that will give them more to think about than "regular not-so-closely related" people? Because maternal identity is never in question, they would be automatically classified as siblings. There are sound theoretical genetic reasons for avoiding marrying your cousin, or your cousin's child because of the risk of genetic diseases, but in this day and age, there are ways to assess those risks for a given pair of people.