As far as I know, this is the case:
There are 2 different schemes that the councils run (in the case of Fingal and South Dublin CC anyway)
1 is the standard Affordable Housing where the council either a), build properties on their own properties or b) where they get properties handed over by the "20% Rule". For this scheme, you take your mortgage out directly from the local authority. You don’t have any choice in the matter.
The second scheme is the Affordable Housing Initiative where a developer hands over a number of properties in a "land swap" with the government (for example Durkans handed over several hundred properties in West Dublin in exchange for some prime state-owned land in the city centre). in these cases you get your mortgage from an "Approved Lender", for example Bank of Ireland. You first get approved to buy an affordable home from the county council, then you need to go to the bank and beg/convince them to give you a mortgage like any other house-buyer
so, in other words, whether or not you get your mortgage from the council depends on which scheme you fall under.
Incidentally, I found that both councils looked very deeply into my finances - I don’t think they are any more lenient than the banks. I dont know if they did a credit bureau check on me, but I presume they did.
I don’t have any loans, so I don’t know what effect loans have on your application. I know that both don’t like over-drafts or large credit card debts - SDCC even asked me to write to my bank and cancel my over-draft.