Some communities, including my own, have the body at home (or the funeral director) for visiting/laying in and there will be round the clock presence (sometimes known as a vigil) until the body is removed to the service. E.g., wakes now often mean a post-funeral event but it's not that unusual for it still to encompass the pre-funeral mourning and visiting.
Judaism has 'sitting shiva' that starts after the interment. Shiva embraces a time when individuals visit the family, giving them an opportunity to discuss their loss and accept the comfort of others. There may be difficulties there depending on whether families accepted a change of role. If a Jewish TW (say) died, would people visiting the family, who may have known the person at different life stages, talk about the person in their memories or the changed status (e.g., from father to mother).
I realise estrangements and people's standing as acknowledged partners with a role in someone's funeral can happen in any family. However, there may well be fundamental splits and disagreements about fundamentals.
It isn't difficult to envisage circumstances in which a partner of the deceased may not always have recognised legal rights to influence the presentation and the clothing choice for the deceased. Nor the booklet that is part of the funeral service, the selection of memories in it, the photographs etc. If there is somebody delivering a eulogy, there can be similar difficulties (where this is religious or humanist). Even the headstone that might end up with a different name, definition of roles (father/mother/sister/brother). Unless somebody opts for a specific, "male presenting NB" status, I don't know what sibling-role some NBs might select.
I am ignoring KM's outmoded use of intersex. I should think most people with VSD want to be left to themselves and not used as political shields or weapons.
None of this includes end-of-life care, of course. So much will depend on circumstances.