Recent attempts to narrow the gap between genders have made positive impacts, however, they created some unexpected backlash effects that might inadvertently hurt women entrepreneurs. Integrating signaling theory and institutional theory, we contend that social impact accelerators (SIAs) can counteract some individual merits of women when they apply to accelerator programs. Thus, we propose that while men-led ventures with external funding have a higher chance of acceptance to SIAs, it does not influence women-led ventures despite greater barriers to gaining it. However, this effect depends on the institutional context. That is, when operating in a country with low gender inequality or high national equity funding availability, external funding matters for both genders. An analysis of survey data of 10,217 startups in 143 countries over 2016-2018 supports most of our predictions. We find while acquiring external funding increases the likelihood of SIA acceptance for men in any nation, in contexts with low equity funding availability, SIAs are more likely to become oblivious to the existing external funding for women, despite the greater challenge in obtaining this signal. Our study challenges the general assumption of signaling theory that signals more difficult to gain will create more value for the sender, informs theories of heterogeneity in resource acquisition in different institutional contexts, and highlights potentially unintended consequences of supporting women.