Well, unless I could possibly find some used budget friendly b4 lenses then any hopes of smooth zooms would be out the window. We don't necessarily "have to" have it as we won't be in a really large space to take advantage of it, but it could possibly come in handy in a few situations. I'm sure we can be more than decent without it. But I guess we'll see how it goes.
That is probably true, yes. And also keep in mind that B4 lenses on any Blackmagic Design camera except the URSA Broadcast require expensive optical converters to even stand a chance of working well.
However, there are a lot of churches and productions that have opted for no servo zoom in exchange for better image quality, better low light performance, more control over the final look/style, a more cinematic look, and/or shallower depth of field and have had great success doing so. Many times the trade-off for a lack of servo zoom is cheaper camera/lens combos and more of them compared to less camera/lens combos with servo zoom. There are also some creative things you can do with your camera ops to get more "energy" or movement without using servo zoom, like giving shots a bit of a handheld look (even on tripods), dollies, gimbals, etc.
Any cameras we purchase would mainly be multi purpose. So do you think it would be wise to still get the IS version and disable it during livestream while on sticks and if needed outside of stream it can be used in that situation?
Yes, having an IS lens is definitely going to be nice to have for non-live production situations. Especially considering that the Blackmagic cameras don't have built-in image stabilization of any kind and are usually fairly lightweight. For sure go for an IS lens if you want to use the cameras for multi-purpose stuff. Just be aware that using IS for shots like tight follow can often lead to distracting movement.