I think you are confusing GST registration with liability to pay GST. I am no accountant or tax lawyer, so do not take my thoughts as definitive advice.
I think you are correct in that your strata plan does not need to be GST registered, as your turnover is under the threshold (which is actually $150,000 for non profit entity) .
Being registered for GST has no impact on the requirement to pay GST when you purchase goods/services from an entity that is GST registered (eg the tradesman who perform work at your strata plan) . Just like you as individual, you are not registered for GST, but you still pay it when you buy fuel, care servicing, clothes etc. You do not avoid GST by not being registered for GST.
Have a look at the ATO website here