In my country, Islamic Republic of Iran, we have a legitimate and Islamic cinema industry by law but one that is carefully regulated by our Cultural Ministry. Film makers are not allowed to legally record movies that endorse, normalize, or promote behavior or thoughts that violate Islam. Since the foundation of Islamic Republic of Iran in 1979 which ushered in a historical opportunity for a full-blown Islamic sociocultural life, thousands of movies have been made for the purpose of promoting Islam, from those featuring the history of Islam to those promoting Islamic faith, ethics etc. Here are some examples:
Therefore our experience shows that not only an Islamically permissible cinema industry can be possible to a very good extent but also that the industry can be even used for promoting Islamic ends.
But outside an Islamic sociocultural community where filmmakers don't or are not required to observe Islamic boundaries (at least on the level of the final outcome), on a personal level, I believe, it is very hard to be in acting job without compromising one's Islamic faith. Because for example in a romantic movie, you may have to act scenes of emotional exchange with a person of the opposite sex which is hardly permissible under normal circumstances (this is even common in our regulated cinema industry in Iran). Or you may have to do things that undoubtedly violate sharia laws, such as shaking hands/hugging a member of the opposite sex, drinking (graver examples of un-Islamic behavior legally forbidden in our regulated cinema), and there is more.
So I'd say, especially in a secular movie industry, you may have hard time acting and at the same time staying faithful to your religious convictions. You may have to be selective, only accepting involvement in those movies that don't require you to act in un-Islamic scenes.