No, if everyone in the world identified as lesbian, gay, bisexual, or transgender (LGBT), it would not lead to human extinction. Sexual orientation and gender identity do not affect a person's ability to reproduce or have children.
It's important to understand that sexual orientation and gender identity are natural and diverse aspects of human sexuality and gender expression. They are not related to reproductive capabilities. People who identify as LGBT can still have children through various means, such as adoption, assisted reproductive technologies, or having relationships with individuals of the opposite sex for procreation.
Human populations can continue to thrive and reproduce regardless of the sexual orientations or gender identities of individuals within that population. The potential for human survival and continuation is based on factors such as reproductive capabilities, population size, genetic diversity, and environmental conditions, among others.
It's worth noting that the scenario you presented is highly unlikely, as sexual orientation and gender identity are deeply ingrained aspects of individuals and are not subject to sudden, universal changes. Human sexuality and gender identity are complex and multifaceted, and a diverse range of orientations and identities exist within the global population.