The skills mentioned in "What is bushcrafting?" sound useful but potentially destructive.
How does bushcrafting relate to the "leave no trace" principles?
The following points for "leave no trace" are taken from lnt.org.
There is not much difference here between bushcrafters and non-bushcrafters, except that a bushcrafter might claim that they are always more prepared just by being a bushcrafter.
Bushcrafters might need to trek back into the bushes at times to get the resources they need, or to perform other actions that violate the spirit of this point.
LNT.org's description of this point also says "Good campsites are found, not made. Altering a site is not necessary." Many bushcrafters will disagree with this. Though not necessary in most situations, many bushcrafters enjoy altering camp to suit their needs.
"Pack it in, pack it out... Deposit solid human waste in catholes dug 6-8 inches deep."
Again, bushcrafting does not necessarily need to violate this, but the spirit of bushcrafting (ie: "be one with nature" and "do as nature does") is somewhat counter to this point.
Depending on what you are doing for bushcrafting, you might generate a lot of waste, possibly too much to pack out. On the upside, the waste is usually all natural, as the waste is generally literally plants, pieces of wood, and stones. There should be no harm in disposing of these materials in the wild, and they can even be safely buried with no harm to nature anywhere you would also use a waste cathole.
Some people have a "do as the animals do" mentality and might leave their waste unburied. This is not specific to bushcrafting, but since the "one with nature" feeling is often higher for bushcrafters it might be more likely. If you encounter anyone like this, you can remind them that even many animals bury their solid waste.
This is the biggest offender. All other leave no trace points a bushcrafter can choose to adhere to by making compromises. But most bushcrafting activities are mutually exclusive with "Leave rocks, plants and other natural objects as you find them." and "Do not build structures, furniture, or dig trenches."
Part of bushcrafting generally requires you to not leave stones and plants as you found them.
Though temporary bushcrafting shelters are often quite natural and often blend in, they are still structures made by moving the resources around an area. And some bushcrafting activities require digging holes or trenches.
Bushcrafters are likely to not use a stove, but the "use a stove" part of this LNT point is more a very strong suggestion than a requirement, as evidenced by the sub-points about wood fires.
The parts of this LNT point about how to have a wood fire are mostly in line with common bushcrafting practices. There are some fire techniques more common among bushcrafters which are not in line with the strict text of this LNT point, but they generally can be done in the spirit of LNT. A fire hole, for example (sometimes called a "Dakota fire hole") can be done such that it leaves a trace similar to a pair of catholes.
Once again, this is mostly in line with common bushcrafting thought, at least on the surface. The sub-point specifically about not approaching wildlife might be an issue for someone who is about to use an animal or its byproducts as part of their craft.
I would view this as similar to hunting, except that it is generally more respectful of the animals than common modern hunting and might not even result in their death depending on what you need (eg: a feather, honey, dung, etc.).
Another point mostly in line with common bushcrafting practice. In fact, many bushcrafters will specifically engage in stealthy camping practices such that other people might not even notice them.
The part of this LNT point most likely to be violated is concerning the noise. Natures sounds might not prevail temporarily if you are making some stone tools.
Overall, Leave No Trace and Bushcraft get along quite well, and most LNT points can be adhered to with a little bit of compromise. Bushcrafting has some minor points on which activities may deviate from LNT, but they are often done sparingly and with respect to nature (or at least they should be), so are often in LNT spirit. The only major point of LNT that is necessarily opposed to bushcrafting in an irreconcilable way is the "Leave the stones and plants how you find them".
What this means to bushcrafting when practicing leave no trace is a priority: bushcrafting must necessarily be limited if you are also trying to practice leave no trace. In areas with sparse resources, you might not be able to practice leave no trace. In areas with a large abundance of resources, you can probably harvest a few resources without risking the ire of strict LNT adherents, but you will need to limit the craft to what you can do with those few resources. No large mud huts, no large kilns or forges, no harvesting which leaves behind a noticeable patch of stem bases, no cracking a bunch of rocks open for tools, etc..
What this means for pure, deep bushcrafting over a very long term in a specific region: Leave no trace is not viable. Lots of rocks will be moved around, broken apart, possibly piled up. There may be holes and trenches in or near camp. Plants need to be harvested in a respectful, sustainable manner but the harvesting may still be very noticeable. For very long term, there is likely to be at least one semi-permanent structure made of stones, wood, and/or mud. There might be other large, visible signs of living such as kilns or tiny dug streams or ponds. It depends on the magnitude of what the person is doing, but it could be quite a mess in and near base camp, and even with a minimalist bushcrafter without all that at best there will still likely be some busted rocks and patches of harvested plants.