My mum left a list of things that were to go to particular people, and a year or so before she asked her children whether there were particular items of furniture they wanted when she didn't need them any more. There were, or course, a lot of little, and not so little, things that weren't on the list. We adult children all got together a week or so after the funeral to sort out and clean her house and at that time, as well as on further occasions, we discussed whether any of us wanted any of the things that weren't on her list. She had some silver cutlery and tableware that weren't on the list (the 'good' items were listed). When we went through that lot we went through the items one by one to see who wanted them and, if there was a difference in value then we ensured that at the end things were distributed more or less fairly. It was just us adult children. We could choose things for our own children, but it was still out of our own 'share'. For instance, my mother had listed some silver cutlery to go to one of my sister's children, but had not listed a canteen of mid-century silver plated cutlery which I knew my daughter would really like to have, so I asked for that. There was one picture she had listed to go to one of my sisters, none of her other pictures were listed but I chose a couple of tiny oil paintings of the Australian countryside and some of the other pictures were chosen by my other sisters. Anything which none of us wanted for ourselves or our children was either went to auction or given to charity. It did help that we all have different taste in things, so it wasn't too difficult to divide things up!
None of the family apart from her own children (and our husbands) were included when we went through her house. All of our husbands kept well out of it when we were choosing what we wanted (they are all very kind, sensible and sensitive men), but they all helped with cleaning, tidying, repairing, touching up paintwork etc.
If you can encourage your parents to think about making a list of what they want to go to whom, eventually, that would really help. Other than that, you need to restrict who comes into the house afterwards until you (adult children) have decided on the distribution of anything that is important to you/valuable. That distribution can include anyone you think, between you, that your parents would have wanted to have something - so extended family, Mabel from bingo, Mrs Bloggs next door etc. After that it you want to you can invite the rest of the family to come and choose something from what is left as a memento of your parents.
I am being treated for cancer and my life-span is limited (death is NOT imminent!) I have already started making a list of the things I own and who they should go to after I shuffle off this mortal coil. I know it will make things very much easier for everyone I leave behind.