We are asking for research that shows that companies like Etsy outperform (on any metric) companies that don't really care about diversity (judged by their actual hiring practices, not paying lip service to it).
Because the availability heuristic points to the other 99% of Silicon Valley that's doing quite well without caring about diversity.
Have you tried Googling? Here are some interesting results (keep in mind science is almost never a home run; that is, you're not going to ever find a study that's like, "We definitively solve this problem for all time and for all mankind"):
https://www.researchgate.net/profile/Stephen_Tallman/publication/228123261_Effects_of_International_Diversity_and_Product_Diversity_on_the_Performance_of_Multinational_Firms/links/00b7d5267dc1adc6d2000000.pdf
http://asq.sagepub.com/content/44/1/1.short
https://www.gsb.stanford.edu/insights/diversity-work-group-performance
http://www.mckinsey.com/business-functions/organization/our-insights/why-diversity-matters
http://www.scientificamerican.com/article/how-diversity-makes-us-smarter/
http://hbswk.hbs.edu/item/why-does-lack-of-gender-diversity-hurt-performance
http://enewsline.aacsb.edu/diversity-in-groups-can-improve-innovation-and-performance.asp
http://www.sciencedirect.com/science/article/pii/S1053482209000795
http://www.sciencedirect.com/science/article/pii/S2212567114001786