You'll get two different but related bugs but yes, assuredly something will break and somebody will be angry about it.
The first thing that'll happen is Let's Encrypt's systems will tell systems by default to present certificate chains which don't mention DST Root CA X3. Lots of systems will, as a result, automatically switch to such a chain when renewing and you'll see a gentle trickle of weird bugs over ~90 days starting this summer unless Let's Encrypt moves the date.
Those bugs will be from clients that somehow in 2020 both didn't trust the ISRG root and couldn't imagine their way to using a different trust path not presented by the server. Somebody more expert in crap certificate verification software can probably tell you exactly which programs will fail and how.
Then there will be months of peace in which seemingly everything is now fine.
Then in September 2021 the other shoe drops. Clients that didn't trust ISRG but had managed to cobble together their own trust path to DST Root CA X3 now notice it has expired on services which present a modern chain or no chain at all.
Those sites which deliberately used the legacy DST Root CA X3 chain to buy a few more months of compatibility likewise see errors, but hopefully they at least knew this was coming and are expecting it.
But there are also sites using crappy ACME clients that didn't obey the spec. They've hard coded DST Root CA X3 not because they wanted compatibility at all costs and are prepared for it to end in September, but because they just pasted together whatever seemed to work without obeying the ACME spec and so even though Let's Encrypt's servers have told them not to use that old certificate chain they aren't listening. Those services now mysteriously break too, even in some relatively modern clients that would trust ISRG, because the service is presenting a chain that insists on DSR Root CA X3 and they aren't smart enough to ignore that.
On the upside, lots of Let's Encrypt certs are just to make somebody's web site work, and an ordinary modern web browser has been battle-tested against this crap for years, so it will soldier on.
The first thing that'll happen is Let's Encrypt's systems will tell systems by default to present certificate chains which don't mention DST Root CA X3. Lots of systems will, as a result, automatically switch to such a chain when renewing and you'll see a gentle trickle of weird bugs over ~90 days starting this summer unless Let's Encrypt moves the date.
Those bugs will be from clients that somehow in 2020 both didn't trust the ISRG root and couldn't imagine their way to using a different trust path not presented by the server. Somebody more expert in crap certificate verification software can probably tell you exactly which programs will fail and how.
Then there will be months of peace in which seemingly everything is now fine.
Then in September 2021 the other shoe drops. Clients that didn't trust ISRG but had managed to cobble together their own trust path to DST Root CA X3 now notice it has expired on services which present a modern chain or no chain at all.
Those sites which deliberately used the legacy DST Root CA X3 chain to buy a few more months of compatibility likewise see errors, but hopefully they at least knew this was coming and are expecting it.
But there are also sites using crappy ACME clients that didn't obey the spec. They've hard coded DST Root CA X3 not because they wanted compatibility at all costs and are prepared for it to end in September, but because they just pasted together whatever seemed to work without obeying the ACME spec and so even though Let's Encrypt's servers have told them not to use that old certificate chain they aren't listening. Those services now mysteriously break too, even in some relatively modern clients that would trust ISRG, because the service is presenting a chain that insists on DSR Root CA X3 and they aren't smart enough to ignore that.
On the upside, lots of Let's Encrypt certs are just to make somebody's web site work, and an ordinary modern web browser has been battle-tested against this crap for years, so it will soldier on.