Gods of the grave watch over the line between life and death. To these deities, death and the afterlife are a foundational part of the multiverse. To desecrate the peace of the dead is an abomination. Deities of the grave include Kelemvor, Wee Jas, the ancestral spirits of the Undying Court, Hades, Anubis, and Osiris. Followers of these deities seek to put wandering spirits to rest, destroy the undead, and ease the suffering of the dying. Their magic also allows them to stave off death for a time, particularly for a person who still has some great work to accomplish in the world. This is a delay of death, not a denial of it, for death will eventually get its due.

It's pretty obvious that the spells animate dead and create undead should be forbidden, but what about the spells speak with dead and spirit shroud?

In my personal opinion, the latter two spells aren't exactly the same as the former. Where Animate Dead and Create Undead manipulate physical corpses into becoming undead, Spirit Shroud and Speak With Dead don't deal with the body- they deal with the "thinking" part of the dead. The Grave subclass as a whole feels more to me like a whole "no touchie the corpses" vibe, respecting the bodies of the deceased. I think it's logical for a cleric that tends to the dead and protects them to have magic that allows them to talk to the departed or ask them for protection rather than just straight-up animating corpses.

I think it also depends on the individual character's view of death, as well as that of their specific deity. My grave cleric wasn't a fan of False Life because it doesn't restore vitality, it invokes a cheap imitation of it. She considered undead to be a profane mockery of life and a blatant disregard of the will of the gods, and False Life was too close to that for her comfort.

Considering False Life is one of the spells granted by the Grave Domain, it makes no sense for a Grave Cleric to forbid it. It also allows one to stave off death for a time, which is exactly one of the purposes of this subclass.

...I just provided my reasons why it made sense for my specific character. Vampiric Touch is also a domain spell I never used because it didn't suit that character. My entire point is that players can add their own flavor to what's appropriate for their character based on their personal view of death and necromancy. 

Quote from theologyofbagels >>

My entire point is that players can add their own flavor to what's appropriate for their character based on their personal view of death and necromancy. 

 That's fair, but I'm looking for spells gods of the grave would forbid, not self-imposed restrictions.