Will the community also dictate who gets what jobs?

The community will not dictate anything, but they will decide who they consider a bum.

Will cleaning the toilets come with the same exchange rate as bending over packing stuff in crates?

Adults are gonna have to adult.
'Pay' is the same for everybody.
You get one share of the all the work for contributing one share of the work.
We all get to order what we want from what is available on the shelf.
IF something you want is not freely available from the warehouses, you will have to find somebody that wants to give you their's.

Will heavy set women get picked to work in cushy office jobs?

You can hire whomever you want.
For whatever reasons that float your boat.

Or will those latter jobs go to those willing to let the choosers stop by after work for some "bible lessons"?

IF you don't like how the community is being run, organize and change it, or find a new one that better suits your purposes.

Freedom isn't perfection.
Perfection is not an option.
All we can do is minimize the necessary impact.

On all days, freedom beats being a slave.