What opinion does Islam have on “acting” as a profession?
In principle all segments of fine arts – including acting and impersonation – are not forbidden by Islam per se if they are adopted as a profession. It is their nature and use which may be objectionable in the eyes of Islam. Thus for example if they do not take into account the gender-interaction norms prescribed by Islam, contaminate the eye and the soul, promote vulgarity or immorality, attack or make fun of the tenets and ideals set by Islam, no decent person can be part of them. However, if such things are taken care of, why would Islam proscribe them?
It may also be pertinent to note that Islam's real message is tazkiyah (spiritual purification) and a believer must always keep this ideal in mind. Things which are conducive to tazkiyah should be sought, relished and adhered to and things which are adverse to tazkiyah should be avoided, shunned and disregarded as much as possible.