I like having some automatic success, but not hard-wired into the main part of the skill system, magic system, etc. Though what I would prefer is probably too reliant on metagaming thinking to satisfy some people.
Namely, what I'd prefer is that characters have an explicit narrative resource which they can spend to radically boost their chances to succeed and/or nullify the need for a roll. And then success percentages are manipulated such that you can't ever get to auto success without this resource (either because of the odds or because a natural 1 still fails no matter what).
So in such a system, dwarves get a small but real bonus to saves versus poison.
And they get the right to use this Auto Success resource to automatically succeed on a poison check. A wizard casting a magic missile normally is highly accurate, but still rolling the check. One that uses the Auto Success option just hits.
Provide several uses of this ability per adventure at 1st level, and have it scale slowly from there. You can still get some nervous nelly DM that thinks climbing a Formosa tree is like climbing Everest, but if you get really ticked off as a player, you can trump his, err, inexperience (yeah, that's the word).
That has kind of a rough and ready parity too it. The DM can say "auto success" because the task you are trying has no meaningful chance of failure, or failure isn't interesting enough or likely enough to even bother rolling. The player can say, "auto success" because this thing right now matters to the player enough to say, "My guy that is really talented in this area succeeds here." The metagame resource keeps a lid on it.
Also, the metagame resource could be shared with some other purpose, to keep even a tighter lid. For example, action points could be used for this purpose.