There are separate issues that get muddled up under this label.
1. There’s a semantic debate among mathematical evolutionary biologists about what the best fitness accounting system is (e.g., inclusive fitness as promoted by the Oxford crowd, or a pluralistic approach favored by most other mebs). This debate will seem totally stupid to economists. This debate shouldn’t be confused with the empirical question of whether intergroup competition has shaped genetic or cultural evolution.
2. The difference between genetic vs. cultural evolution, and between cultural group selection and genetic group selection. Many researchers like Boyd and Richerson have argued against the importance of genetic group selection for humans but FOR the importance of intergroup competition shaping cultural evolution. Much modelling suggests that conditions that normally inhibit the importance of GGS in genetic systems are mitigated in cultural evolutionary systems–because of multiple stable equilibrium (think folk theorem with different populations stuck at different equilibrium)
3. Empirically, a lot of evidence suggests that intergroup competition has shaped cultural evolution (institutions, social norms, religions, etc.)
Two recent target articles in BBS with full commentaries and replies are the places to start
I would avoid the opinions of web-publishing non-experts, who have not contributed to the primary literature and don’t understand cultural evolution.
In general I thought the comment thread on group selection was excellent.