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There are always going to be those snob music directors who simply will not hire you if you don't already play upright, and in my area, there are those, typically alumni of a university music school that think there is only one way to do things. To me, bass is bass, it can be done with bass guitar as well. The most important thing is to get a good sound, play well, and enjoy what you're doing. You really do have to love music theatre to put up with some of the vexations of the productions and do this over a long period.
There are a myriad of situations/shows calling for arco upright bass (Sondheim shows immediately come to mind), and if the show is being produced at an Equity or other professional level, expecting the person hired to play the bass chair to play upright is far from "snobbish" or unreasonable. While bass guitars certainly have a place in jazz ensembles, including Buddy Rich's big band, there is plenty of literature and situations where upright bass is a much, MUCH better fit, and again, there's nothing snobbish about that...simply fact. I wouldn't bring my electric violin to a string quartet gig.A bit of a thread derailment, but need to call out that these types chased me away from playing in my school's Jazz bands in college. College I went to had several Jazz bands, but they only played older big band Jazz pieces. I learned double bass to play in the band for a year and quickly became tired of the music. To the "academics" at that school, Jazz stopped in the 40s... which is crazy to me.
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If we're talking community theater, amateur pit, or situations where compromises are welcomed, then fine and no worries. As long as everyone's happy, great. I just take exception to calling anyone snobbish for suggesting the correct instrument be played if possible. "A bass is a bass" isn't any more true than a car is a car or a house is a house. The differences are vast, discernible, and important.