Despite the clearly partisan claims of people who don't like the current President, this question is NOT a duplicate.
I have been seeing more and more the word "President" being used without capitalization lately. Specifically, this appears in what used to be respectful newspapers (NY Times and such). Is this their use of poetic license to show their dissatisfaction with President Trump? Or is it a more subtle point?
My understanding was that when referring to an office which is held by one person at a time, the title of the office is always to be capitalized because it's a proper name. But I don't even remember the last time I saw NY Times capitalize "President". What's a good rule of thumb? In my own writing, I've followed the rule that if the word is plural or if the article "a" is appropriate, then the word should be lower-case; otherwise, it should be capitalized.
To be clear, the context in which I see these lack of capitalization is one in which the current President is discussed and his specific actions are being addressed and they are not being compared to actions of other presidents.
Edit: thanks to Mari-Lou's findings, I have to concede the recent practice at NY Times has been to only capitalize "President" before a proper name. However, the links I have found show that they used "the President" as recently as the Clinton era and began changing to "the president" starting with Bush.
Edit 2: User Nat found that the precise time of the change was actually in the last year of Clinton's administration.
Interestingly, they still had to use "the President" during the Bush administration when referring to proper titles of books they reviewed and when publishing historic accounts. In fact, even if parts of those accounts were their own text joining multiple narratives they used the historical papers' grammar rules.
I'll post some of what I found in the hopes that some people may find it interesting and maybe even elucidating. Unfortunately, due to the would-be political hackery of those who don't like anything short of the sharpest rebuke of the current President, this question (about grammar of all things!) is now wrongly marked as a duplicate. As a result, I cannot post the part after the "edit" as an answer to my own question (because no further answers can be posted).
Here's some examples of how the grammar at NYTimes has evolved:
The 2 example below are due to a comment by Nat:
2001 review of 4 books, titled "The Making of the President, 2000", has NYTimes' byline and clearly it is still using "the President" in the title, but already switched to "the president" in the text.