My chain is well over the 0.75% extension at which I would normally replace it. However, the cassette and chainrings are also old enough that a new chain would slip on them, so they would also need to be replaced.
The drivetrain currently works, despite being worn, so there doesn't seem much point in replacing anything yet.
How long should I leave it before replacing the entire drivetrain?
How long should I leave it before replacing the entire drivetrain?
There is no way to provide a definitive answer, its akin to asking: "How long can I smoke before increasing my risk of getting cancer?" We know your risk of certain types of cancer increases with smoking, but it is impossible to predict exactly moment individual will develop cancer as it is also a random outcome (i.e., smoking is altering the probability of the cancer outcome).
In a similar manner, we know certain negative outcomes are more likely to occur on a well worn drive train (see other answers) than a drive train that is within specifications, but it is impossible to reliably predict exactly when these will occur an individual case.
From experience I would be most concerned with the increased risk breaking a chain as this can potentially lead to a dangerous accident. As the the drive train wears shifting deteriorates. Users often jam shifts more frequently as a result, which in turn put added strain on the chain and can lead to subtle bending of the link outer plates. A bent link plates mean a weaker chain link which can increase the probability of snapping a chain link under power (e.g., sprinting for a light, climbing out of the saddle). If you have ever had a chain suddenly snap on you, then you will know it can throw you from the bike, or cause you to swerve severely to correct for the sudden loss in balance. If either of those happen at an inopportune moment (e.g., with passing traffic), you could end up in a potentially life altering or life ending accident.
Again all this is about risk management. Your bike does not suddenly turn into a death machine intent on your demise the moment chain reads 0.75%. Rather the chain has been slowly weakening due to wear over time, running it out past 0.75% means chain is already weaker, plus the cassette and chain ring teeth will now experience accelerated wear (due to the chain is out of specification), which in turn can further hasten the chain's wear and demise.
Whether or not you should replace depends on your risk tolerance. If you do not want to accept any increased risk, then I would replace immediately. Otherwise, I would monitor the chain's behaviour and replace when the shifting starts to noticeably deteriorate. I would also ride with the knowledge that you can no longer fully trust the chain anymore and would avoid any sort of sprints, especially out of the saddle.
Finally, I wanted to address chain slippage (as it is also mentioned in various answers). Typically occurs when one mixes drivetrain components with different effective pitches (e.g., new chain on a worn cassette). Because the cassette, chain, and chain rings are all worn, the effective pitch should be fairly similar meaning that there should not be any immediate concern for slipping. That said, if the drive train does become severely worn (e.g., losing the top of the tooth profile due to wear) then slippage can become a issue in addition to breakage. My anecdotal experience has been that chain breakage is however much more likely. That said, either type of failure can cause the type of accident described above.
The problem with worn, stretched chains are: increased wear on the cassette sprockets and chainrings, poor shifting, chain slipping on the sprockets, reduced efficiency and increased chance of the chain snapping.
Normally it's considered 'safe' to run a chain up to 0.75% elongation before risking encountering those problems. If you really care about sprocket and chainring wear replace at 0.5% elongation.
If the sprockets and rings are already well worn and everything seems to be working OK for you, just keep going until problems really start to manifest or something fails terminally, at which point you replace the cassette, rings and chain in one go.
Chain slip or the chain snapping could of course put you in actual danger of a crash, especially as both are likely to happen when you are applying maximum force on the chain in a low gear ratio.
If the chain starts slipping on your current chain rings and/or cassette, you should replace it straight away.
I'd recommend replacing it before then.
If you replace it before it becomes an emergency, you get to replace it at a time that's convenient for you. This is especially important if you use the bike, e.g., to commute or in some other way that means you need it to be reliable.
When it does start to slip, it's most likely to be when you stand on the pedals to put down some power up a hill. The chain slipping and the pedals turning with much less resistance than you expected is dangerous and might cause you to fall.
While you may be able to adapt your riding style to minimize the problems caused by this worn drive train, if anyone else ever rides the bike, they should have a bike that works normally, rather than one that requires techniques you might not even realise you've been gradually learning for however long.
