As societal acceptance of LGBTQ rights grows, corporations face increasing pressure to reflect these evolving values, not only internally but also through public advocacy. Public support for LGBTQ inclusion can enhance a company's legitimacy and innovation by attracting diverse talent and fostering a supportive culture. However, merely expressing support without aligning internal policies may lead to perceptions of insincerity. This study investigates how corporate public support for LGBTQ inclusion affects corporate innovation and examines the moderating effect of internal LGBTQ policies on this relationship. Drawing on Legitimacy Theory, this research proposes that authentic consistency between external advocacy and internal practices strengthens stakeholder trust and enhances innovation outcomes. The study analyzes data from 472 companies listed in the 2021 Corporate Equality Index (CEI). It uses patent filings to measure innovation, the number of #LGBTQ tweets from official Twitter accounts for public support, and CEI scores for internal policies. The analysis confirms that public support for LGBTQ inclusion positively impacts corporate innovation. This effect is amplified when companies have robust internal LGBTQ policies. These findings highlight the importance of aligning public advocacy with internal practices to build trust, attract diverse talent, and foster an innovative organizational culture.