Less flexible people may not be able to march into a yoga studio and immediately touch their toes, but that doesn't mean they can't attend yoga classes. In fact, some sources encourage inflexible people to take up yoga in order to improve flexibility and mobility.
Yoga tends to be an inclusive practice, and individuals who are inflexible due to a disability, injury or age may be able to find a yoga studio or instructor who works slowly and takes these limitations into account during a session. In fact, there may even be some yoga classes specifically designed for people with limited mobility.
Seeing an experienced yogi twist him or herself into all kinds of positions can be intimidating for people who have never before tried to test their flexibility, but these individuals have likely been working at their practice for a long time. Yoga views flexibility as a skill that can be developed over time. Beginners who are nervous about their flexibility should try a beginner's class, where there are likely more people on the same level.