Golem into dust
There is nothing in the language of disintegrate that suggests that there are certain creature types that are immune to its final effect.
A disintegrated creature and everything it is wearing and carrying, except magic items, are reduced to a pile of fine gray dust.
Because of that, it does suggest that the spell works on all types.
The terms of this feature seem to suggest that its immutable form is more to protect it against polymorph spells and other form-changing magic/abilities.
The turning to ash upon death from disintegrate isn't really about changing its form - it's about destroying it's body once killed.
While there could be a case that destruction of the body falls under Immutable Form, it makes more sense to look at the ability as something that prevents it from being converted into a different creature and not something that prevents its total destruction upon death. While Crawford's ruling is not RAW, I think the interpretation of destruction not being equivalent to shape change makes sense and his tweet below supports that.
Jeremy Crawford on Twitter:
A golem, like other constructs, is a creature. In fact, all the monsters in the Monster Manual are creatures. When a spell, such as disintegrate, says it does something to creatures, the spell means a creature of any type, unless the spell makes exceptions.