I find this a very difficult topic, especially with the second 8th Ed Codex: Space Marines. As a general rule I am happy for people to test out different codices or to count Successors as the actual parent Chapter for rules purposes (otherwise you run into situations like the one below); I am less comfortable with fully-painted Imperial Fists running as Salamanders (or worse, Chaos warbands using Imperial rules!), whilst running Tyranids as Blood Angels would be right out.
So, the absurd scenario of some of the successor-versus-parent rules I alluded to above:
I am quite interested in various Ultramarine successors, for example a Black Consuls Primaris rebuild, or a variant colour scheme of the Ultramarines that looks stunning (effectively Veteran Intercessors) and I would have to come up with my own background around them. I don't mind not having access to the full relic list since Warlord Traits, Psychic Powers and Stratagems are far more defining in my mind. I don't even mind not having access to the special characters like Marneus Calgar or Tigurius
I would however like to use the Guilliman model I have as a centerpiece, in massive games with a true UM retinue. This goes back to the fluff of Guilliman leading the Indomitus Crusade (my army is exclusively Primaris) and the Ultima founding successors serving directly under his field command. He'd be proper Guilliman in Ultramarine regalia, genuine Victrix Guard and so on, within his/their own specific Detachment.
According to the rules as they appear to me (and part of a thread in the Official Rules forum), I could give my BLACK CONSULS the Ultramarines successor rules (be it Inheritors or two chosen traits) and pick up Scions of Guilliman thanks to being the UM successors. Running my army as pure ULTRAMARINES gives them Scions of Guilliman. However, if I put the big man himself on the field alongside the successor, everybody forgets they're his Scions thanks to the specific wording, so taking their liege-lord actually makes them worse adherents of their own chapter rules. Heck, even his Ultramarine bodyguards suddenly forget they are his lineage!!
The only way around that is to counts-as the whole lot of <whatevers> as ULTRAMARINES so they don't suddenly forget their genetic lineage. But I don't want to do that since it, personally, cheapens the background of the chosen successor and feels a bit "That Guy"-ish