If by scripts you mean “written texts” (and if you do, it’s a misleading way of saying it), languages evolve mostly through the spoken word. However, peculiarities of written registers can influence how people speak—for example, the reemergence of /t/ in often, or the influence of Classical Arabic on the spoken Arabic variants.
Written language can exercise a conservative effect on how the language evolves overall. That is exemplified most clearly in Icelandic, but there’s a good argument to be made that it applies to American English and British English remaining more or less mutually intelligible.