The involvement of companies and public institutions in open-source software (OSS) has become widespread. While studies have explored the business models of for-profit organizations and their impact on software quality, little is known about their influence on OSS communities, especially in terms of diversity and inclusion. This knowledge gap is significant, considering that many organizations have the resources to enhance diversity and inclusion internally, but whether these efforts extend to OSS remains uncertain. To address this gap, we conducted interviews with maintainers of community-owned and organization-owned OSS projects, revealing tensions between organizations and their projects and identifying the impact of internal policies on OSS communities. Our findings reveal that, on the one hand, organization-owned projects often restrict external contributions due to stringent operating procedures and segmented communication, leading to limited external engagement. On the other hand, these organizations positively influence diversity and inclusion, notably in the representation and roles of women and the implementation of mentorship programs.