And does this apply to all resources that can be harvested or only to forests?
Basically the same principle counts. It is however important to consider the real value of the resource. If you have for example a minable resource on a hill, you can harvest it and the hill will still be a minable tile. It will just provide 1 less production per turn for the rest of the game. If however you are going to remove a minable resource from a flat tile, you turn a productive tile into a non productive one. You give up the opportunity to have a mine there that would not just provide 1 production per turn, but would produce more as the game progresses. Having a productive tile for each of your citizens is also very important.
"hop as soon as you can to boost your production and advance more quickly. Having something
now is better than having it later."
This statement is one that is imo a bit too strongly worded. As it is too easy to make you believe you need to cut everything asap. So that is the "not sure if everyone will entirely agree" part
If you are taking that cut sooner rather than later too serious, you would end up cutting and harvesting everything as soon as it comes into your lands. Much of the production being used to build the workers that do the next cut, turning it into a cascade of workers and cleaning out all of your lands. I think we can all sense that something is not entirely right here. Now you can just look at the inflation argument and say "but the math sais it's right, so im just being emotional instead of rational" but i don't think that is entirely correct.
I think you need to realize that we are here, looking at one side of the equation and simplifying things. We are here looking at everything from the inflation perspective. One that i fully support, one that only few players really seem to grasp by themselves. Therefore, it is good to hammer home on this as it may well be a key insight for many people to make leaps forward in their game. It doesn't only apply to chopping/harvesting. It for example also explains why most (read all but rare exceptions) wonders are a bad investment.
The other side of the story is however one that many players understand, especially those that have been playing strategy games for a long time: The concept that your primary goal is to actually create this compounding growth. That you want to invest as much as possible in growth. Harvesting/cutting resources seems to be the opposite. And it IS the opposite if you are not using that production on something else that really adds to your long term growth.
It's probably obvious to anyone that you don't want to harvest resources if you don't have anything good to build. But consider the following situation: You are building an industrial zone. You have the opportunity to cut a forest or harvest a resource. So you cut it, and finish the IZ 3 turns sooner. Great. Next you build a workshop, it is also 3 turns earlier. Awesome, this is why we do it right ? However, now you don't have the technology to produce anything meaningful, so you continue building that granary you don't need. Or maybe you build a few extra units you don't really need. This means you pretty much wasted the harvest. You gained 3 turns worth of IZ and workshop production, but now you are producing useless crap, so you lose it again.
Also look at the actual value of the cut. It's much more complicated than it seems on first sight. The game starts. You build a worker for 50 production. You can now cut 3 forests for how much is it ? 24 production each ? Seems you have gained 3x24-50 = 22 production. But don't forget that:
-This doesn't happen in a single turn. It took a bunch of turns producing the worker, and then a bunch more to move it around. According to the inflation theory itself, that already reduces the value of these cuts significantly and quite likely enough to lose out all of that 22 production you think you gained.
-You increased the price of every future worker you will build.
So the reality is that you basically start out at a negative gain for cutting, and it gradually grows troughout early game. In late game, the value declines because whatever you are using that production for is no longer significant to help you win the game. Somewhere during the game, the value peaks. I can't tell you exactly where, but i am sure it's not in the first 20 and not in the last 20 turns. My intuition sais @feudalism. But everything that goes into analysing and reasoning it is too much to back that up with math and this also surely is too simplified. More likely it is optimal to use some harvest/cuts at the key moments for your early expansion, then use some to assist you in your early district discount planning, then use some @ feudalism, finally use the last ones for your spaceport if you are going that way.
Just a few things to make clear that it is not as plain and simple as it can be stated in a few simple rules or guidelines. The fact that we are still discussing this shows that it is not as plain and simple as can be explained in multiple forum threads with some of the best players and theory crafters this site has to offer. You will have to think for yourself, and combine all the knowledge you read. You will never be a great player by following simple rules and guidelines. And this is what makes civ great. In starcraft1, we had very simple rules (always be building SCVs from each of your CC's unless you have more than 80, never build any static defence ever) Civ6 is too complicated for simple rules.