Given that the Doctor is careful about not changing established history when travelling into the past [certainly the First Doctor in the Aztecs was quite adamant that history couldn't be changed, though this view softened and the concept of "fixed points in time" was introduced], how does he ensure that he isn't going to change the established history of the times even further in the future of the period he is in [in the tenth Doctor's second story the Doctor wouldn't attempt to save the Earth from being destroyed]? Namely, if he travels to the future, this future is someone else's past.
While I was looking up some examples, came across this on the Wiki page for Kill the Moon: "In "The Fires of Pompeii", the Tenth Doctor says that as a Time Lord, he can see both fixed and mutable points in time. The Twelfth Doctor says the same thing here, but that there are "grey areas", points in time for which he cannot see the outcome.", with a link (and this is just my point of view, perhaps a little unfairly since there were some good moments, misnamed) to the site.
There's quite a bit of evidence from the show that the Doctor has been to points in time from every period of the Universe, across multiple alternate timelines, collecting information as he goes. Consider that his relationship to River Song across the ages proceeded backwards in time from their first meeting, for instance. The history of Gallifrey before its fall occurred very far in the future from present-day Earth, and may even be connected to present-day Earth's fate in the far future. So almost everything in our future consists of events in the past from the Doctor's perspective, and even then they go towards the end of the Universe, time-wise, the Doctor appears to have the same concerns about not disrupting events that are supposed to make history (in the far future), unless he is prophesied to have been part of those events (which he often is).
I think we need to look at this more four-dimensionally.
"The history of the future" is going to be relative to any one person at any one time. Technically, everything we do right now "changes" the future in some way, up to and including whether or not I finish replying to this post. But since we don't know anything about the future, we've no idea how we're changing things.
So for The Doctor, everything (s)he does affects events past the point that (s)he arrives.
(That's gonna get tiring - let's go with "she", shall we?)
If she knows nothing about the future of any one person (from someone she saves to one of her companions), she's got no idea what she's doing to the future. In the case of, say, Adelaide Brooke and the staff of Bowie Base One, The Doctor knew damn well who they were, and what was to happen, knew not to do anything to save them, and did it anyway.
One of the best examples of affecting "the future" was the Hartnell adventure The Ark. They arrive on a generation ship twice, many years apart, and the results of their first visit (leaving behind a cold virus) had catastrophic effects on the people of the ship by the time of their second visit. The Face of Evil is another example - bad computer programming resulted in societal upheaval.
So to summarize, The Doctor only seems to worry about how she's affecting things when she's AWARE of what the future of those things are. If she's no idea, she works under the assumption that having good people not die is the best strategy.
(Hope you enjoy being in this post completed comment timeline)