I`m in a similar position, my tone is very twangy and driven, to DI it before my DI Pedal (what a novel idea, eh, have had someone try) would decimate the sound of the band. Nothing wrong with a regular Precision sound, but putting James Jamersons sound into my band, where my sound is more like JJ Burnell, well which rocket surgeon would think that`s a good idea? Oh yeah, someone that`s never heard the band before, but "knows the room".
Luckily I`ve only encountered a couple of people like this along the way in my current band, out of many more than 100, so it`s not something I`m that concerned with. Plus most of the venues we play are venues for our type of music, so the sound-people know what they`re doing on this genre anyway.
I think the main thing though, is knowing what you are sending to FOH, and keeping the signals even, no volume spikes due to badly thought out effects etc. Most of the time the sound-people will recognise when someone knows what they`re doing - or is bluffing well in my case - so they`re happy to go with what the bands want.