Where is the exclusivity concern coming from? Just that you're closed for a night?
If the shop needs a night to focus on getting builds done, then do it. It's pretty common for co ops to not have time to complete builds during normal shifts.
Whether those builds/sales are necessary for the shop to work financially, I'm guessing those bikes fulfill your mission. I'm guessing that they're being sold at fair or below prices to people who might not otherwise get a bike.
Not all volunteers want to deal with helping others in a face to face way but still want to give back. Plenty of volunteers would rather work on fixing a bike, knowing it will later improve someone else's life, without needing a direct interaction. This often includes marginalized groups who would otherwise not volunteer.
I know many people who "afford to volunteer their time" specifically because they cannot afford to pay full price for shop time and parts but want to earn their way rather than using our sliding scale. Without volunteer night their time to work on their own bike would be greatly reduced.
> to build bikes at the shop to sell to the public
Going a step further, it's very common for co ops to have volunteer only nights to work on their own bikes. This is seen as a perk of being a volunteer and could be said doesn't directly benefit the co op. However, I don't think this practice falls under "inequitable and exclusive" either. It's not possible to have a co op open all the time, so these nights generally fall when the shop would otherwise be closed. It helps retain volunteers and keeps regular shifts running more smoothly as volunteers can focus on their shift.
I would say that one volunteer night per week actually makes the co op more "equitable and inclusive" rather than the opposite. Besides, don't let good be the enemy of perfect, especially on the smaller points of things.