Startup affinity banks that have proliferated in recent years—targeting all sorts of underrepresented groups, from immigrants to LGBTQ communities—might seem like small fries compared to the big, traditional banks. But a new study by Deloitte says that collectively the newcomers are a real threat, especially if the big banks don’t step up their efforts to advance social equity.

Indeed, consumers, especially younger ones, increasingly expect businesses they associate with to operate in a socially responsible way and advance social justice, sustainability and other causes they deem important, according to the report, which was based on a survey of 2,000 respondents across the United States.