Hi Paul, I do agree with the fact that phrase like ‘it’s raining outside’ are some kind of tautology because it can rain outdoors only. As for the difference between ‘out’ and ‘outside’ I think that we usually use ‘out’ either as part of a phrasal verb as in “Let’s go out tonight” or “He just walked out on me”. Usually, ‘out’ describes some kind of movement while ‘outside’ refers to a location. I have never heard the phrase “It’s raining out” but then again I’m not a native speaker of English. Lets’ see what @Alan and @Andrea have to say on this.
By the way, welcome to the forum and thanks a lot for bringing up this interesting topic. 
Here is some more information on the topic from StackExchange:
“outside” is a location relative to where you are (presumably, you are inside), so in all three of your samples, ‘outside’ is the normal choice.
“out” is usually directional, So your ‘It is raining out’ would be probably understood as it is raining inside but some of it is leaking through the walls / windows to the outside world (this is far less likely to happen in practice than ‘It is raining in’).
A less common use of “out” would be as a comparator; as in “He stood out from the crowd”, meaning he was different from the rest of the people even if physically located amongst them."