As I wrote in my article, there are many theories on this subject. The one that you end up in a different timeline is viable, and also one of the most popular ones.

And when you mention the air molecules, this is a valid point too. In order for the time loop to be consistent, there shouldn't be air molecules there in the first place, it should be you. If you know that you weren't there, or that fact has any effect on the present state of the universe, then trying to go back in time and appear in that place makes the time loop inconsistent, and shouldn't be possible (or should lead you to a different timeline, as you suggested).

Also,

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The classic example being that you kill your grandfather before you are born

This won't work, you need to kill him before he has a child who is one of your parents.

It could also be that some changes made by the time traveler are below the "noise level" and do not really impact anything.

Also, for it to be a paradox, the change has to be something that would affect the traveler. For example, if I go to the past and kill a famous person, the news of his murder would be in newspapers and I should have known about it before I went to the past. If he was alive in my original timeline, that's a change that affects me (I know information that was valid, but is no longer valid because I changed the past).

On the other hand, if I go to the past, stay in the middle of nowhere for a while and come back, the past would now have a little bit less oxygen and a little bit more carbon dioxide, but the change would be below "noise level" and, while it may affect the "present" in some small way, it would not affect me or my knowledge (unless I had the exact composition of air measured down to the molecule).

The same probably applies to going to the future - if I go to the future and bring back lottery numbers, it would probably be a paradox, because I could have read an article in the future about the lottery and it could mention someone else winning it (but now I'm going to at least share the jackpot with him). On the other hand, if I bring back stock price charts, I probably could invest some money and get good returns without actually affecting the prices that much (if I buy $20k of Apple shares, it would not really move the price, especially if I brought back the cart that shows a price increase because of some event - new phone announcement etc).

At least that's pretty much how fiction operates, there is no way to know how "real" time travel to the past would work.