I removed the grate from my cast iron floor drain (in basement) and
found that the internal cap (mushroom shape) had rusted off and was
just sitting in there. What's left is the cup with the pipe in it and
the grate. It looks like the trap is in good shape as there is some
standing water visible in the pipe and there is absolutely no smell of
septic gas.

My question is this - if this drain is in an old shower stall that I
want to use while remodeling the main bathroom, is it ok to use as is?
Water seems to go down properly and I got an initial estimate of $350
to replace. I don't want to have to remodel this bathroom so that I
can remodel the other.

Thanks in advance...

It will probablyt be ok, but the worst rust in under the normal
standing water. My 50 year old 4 inch pipe was so rusty a snake wouldnt
fit thru there.

Just sop you knpow the condition I would use a wet dry shop vac to
remove the water, and take a look, that pipe is likely less than a inch
opening it the other piece rotted off.

its a lot of work but can be replaced DIY with plastic, that will never
rust