Distance from the star
The distance between a planet and its star is one of the most important factors in determining whether or not the planet can be habitable. If the planet is too close to the star, it will be too hot for liquid water to exist on its surface. If the planet is too far from the star, it will be too cold for liquid water to exist.
Star's luminosity
The luminosity of a star is also an important factor in determining whether or not a planet orbiting it can be habitable. Red dwarfs are much less luminous than stars like our Sun. This means that planets orbiting red dwarfs must be much closer to the star in order to receive enough heat to support liquid water.
Planet's atmospheric composition
The composition of a planet's atmosphere is also important in determining whether or not it can be habitable. Planets with atmospheres that are rich in greenhouse gases, such as carbon dioxide and methane, can trap heat and make the planet warmer. This can help to compensate for the fact that planets orbiting red dwarfs are typically much closer to their stars than planets orbiting Sun-like stars.
Other factors
In addition to the factors discussed above, there are a number of other factors that can affect whether or not a planet tidally locked to a red dwarf star can be habitable. These include the planet's rotation rate, the presence of a magnetic field, and the presence of water on the planet's surface.
Conclusion
The question of whether or not planets tidally locked to red dwarf stars can be habitable is a complex one with no easy answer. There are a number of factors that need to be considered, and the answer may vary depending on the specific circumstances of each individual planet.
