It is possible to visit the facilities of the Roque de los Muchachos Observatory, but only upon prior reservation and only in the morning. See “Visits to the Observatory” on this website.
However, under no circumstances is it possible to stargaze at the observatory at night or to visit the observatory in the evening. From sunset until dawn the gates at the observatory are locked (20:00-7:00) are and only professionals are allowed. For stargazing tours see here.