Remakes are irrelevant to my judgement of an original film. The remake/reboot is a separate creation. However a sequel is different as this is the continuing story of the original. The final season of Game of Thrones ruined the whole series for me, but really as a rule, it depends how close the story links are with the sequel to the one before it. If I only like original Star Trek, then everything after this can be easily someone else's 'What Ifs' and I don't have to accept it, as after all it's only fiction.