I have changed the chain after my gauge showed that it's .75 worn. New chain jumps anyway. Why? How to deal with it?

The general rule does seem to be 2 chains to one cassette. However, if you ride a great deal on a couple of sprockets they may be worn out more than the others.

Take a good look at the cassette to see if any of the sprockets are worn.

Don't panic.

Let's suppose you got the correct type of chain, mounted it correctly (aren't 11sp directional?), checked your rear derailleur is well adjusted. Then it is possible that the two suspect cogs are indeed worn. Do look at the cassette from the side and determine if their tooth shape is different from, say, the largest one.

If they are indeed worn, what will now happen is that your new chain will rapidly wear to a state similar to the old one. As now the chain is longer, it will stop skipping over those cogs. You will be able to get some mileage on it, before it hits the 1% mark and become damaging to the front chainring.

If the 2 smallest cogs are indeed worn, I can imagine possible reasons, which have caused it:

• Very gritty drivetrain. Ruled out in your case.
• You ride only on those cogs. Like riding a mountain bike exclusively on road. But I doubt 1500km would be enough to wear the cogs with an unworn chain.
• You constantly overstress those cogs. Like riding standing uphill or somehow managing to drop your weight on only one pedal when landing from jumps. Do think about your cadence when riding.

Also I have heard the rule as 3 chains per cogset and 3 cogsets per chainring. As you see, not too often.

My experience, although not with a 1x11 drivetrain, is that the chain very rapidly adapts and stops skipping. Recently I replaced the chain of my 10-sp Campagnolo Chorus drive train. Initially it skipped frequently, say >10 times per km, on the 17-18-19t cogs, which is my usual comfort zone. After riding in a strong headwind on 21t for about 30 km and return with a tailwind on 15-16t, surprisingly the skipping on 17-18-19 had almost disappeared. After another two 60 km rides the skipping has stopped completely.

I expect that probably next time the chain is worn, say after 5000 km (road bike), the trick doesn't work and I have to replace the cassette.

So my advice is to go out for a ride in which you don't use the cogs that cause skipping. See what happens after that. Perhaps make some intermediate statistics in which you do use the bad cogs and count the number of skips. Might be interesting feedback.

I don't think your chainring will be harmed from this. It will wear according to the actual chain elongation, independent on whether you renew or not renew the cassette.

The previous answers appear to have missed the fact that with 11s and higher drivetrains, the current consensus appears to be replacing the chain once it hits 0.5% wear. At .75%, riders will frequently need a new cassette. While this obviously seems expensive, many 11s and higher cassettes are even more expensive. On the road, our outer chainrings are also very expensive, and we really don't want to wear those.

In comments, the OP said they used a dry lubricant. Dry lubes contain some lubricant, usually wax-based, in a carrier fluid. The fluid evaporates. Some empirical testing has shown that many dry lubes are poor lubricants. White Lightning's dry lube is a particularly clear example: if you examine a bottle that's been sitting on the shelves, you'll see that it's mostly a clearish fluid, and a small amount of residue at the bottom. The residue is what dries off and lubricates the chain. In a wear test of White Lightning Epic Ride, Adam Kerin agreed that it made for a clean running drivetrain. The price of this was one of the highest wear rates he has tested. He described the test chains as sounding dry very quickly, which is an indicator that there is not much actual lubricant in the chain.

High-performing dry lubes (i.e. produce long chain life and low drivetrain friction) do exist, but they require very thorough cleaning of the chain before application. This involves repeated solvent baths, and preferably removing any solvent residue with an alcohol bath afterward. I think that the OP's choice of a dry lube probably shortened their chain life. I would suggest switching to a good wet lube. If the OP just does the same chain cleaning routine described in the comments, I bet this would produce markedly better chain life.

If the OP wanted to go one step further, I think that an on-bike chain cleaner is relatively simple to implement. I am not sure how much difference wiping the chain with degreaser on a rag makes; what you ideally want to do is to get the dirt off the chain surface and out from inside the chain, at least as much as possible. A rag and degreaser shouldn't clean inside the chain. I'm not sure if it will remove more dirt than simply wiping the chain.

Fun fact: in chain wear testing, i.e. when comparing different chains (as opposed to different lubricants) for durability, Kerin now uses White Lightning dry lube to shorten the chain life, so that he can complete the tests in a reasonable interval. To my knowledge, he only has one test rig.