Is it permissible to perform Tayammum for entering the mosque and performing prayer when there is a fear of contracting an infection due to weak immunity?

It is not permissible to perform tayammum (dry ablution) except when water is unavailable, or when there is fear of harm from using it. If you fear harm from performing ablution in a public place, and you cannot find another place, then tayammum is permissible for you. The fear of harm must be real, not merely an illusion, and it should be based on the statement of a trustworthy doctor or personal experience.