
Seisho |

That...is actually a really good question since one does usually have only one kind of fingernails
if you consider having them both ask your gm, you might have one hand with the one kind of claws and the other one with, well, the others (or hands and feet? this gets a little weird)
but usually I would say you have to decide for one setting of claw attacks and since slag may is a lineage feat the are probably the 'dominant' one and disqualify you from hag clows
if you gm is very generous the might stack to a d6 finesse, agile, grapple, cold iron weapon - but I would not rely on that

Abyssalwyrm |

Slag May you can pick only at level-1, as it is a lineage feat.
Hag Claws you can gain at the any level, as long as you are changeling heritage.
Obviously if you already have one type of claws - you won't be able to grow the other.
Even with the races that can have a claws (like a catfolk for example), so far they gaining claws only through a heritage.
So even picking such bizarre combination as Catfolk/Changeling/Slag May, only one instance actually would grant you claws. And as usual you obviously wouldn't be able to grow more claws.

Mellored |

"Sometimes a versatile heritage might give you an ability that conflicts with an ability from your ancestry. In these cases, you choose which of the conflicting abilities your character has."
So you need to choose.
Though given you spend a feat on a duplicate feature. I would allow a changing to choose at-will, with an interact action. Basically treat them as 2 different weapons.
Also kind of flavorful to have your claws morph.

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That...is actually a really good question since one does usually have only one kind of fingernails
That doesn't mean you have only one way to attack with them. Monks and Barbarians can easily have multiple ways to attack with their fists.
That said, these are mostly redundant so I probably just wouldn't take both. They are both first level feats.