Let's try to sum up your points so they can be addressed 1 by 1. I haven't used Erlang but I have done a fair bit of Elixir now.
"it can't actually do anything that other many languages can't do too"
I personally think it's really difficult to scale systems without loosing messages. Having the OTP available in GenServer and GenEvent in Elixir is amazing and provides a nice way of creating your own servers. A good example of these primitives in use is the Redis Driver; it uses two processes - one to send messages to Redis and one to Receive them. This means that essentially all messages going to redis are performed in a set and forget way. Most other clients (even in erlang) block and wait for a response from redis.
Now I am not saying that it's impossible to write this stuff well in other languages/virtual machines but I am saying that Erlang/Elixir/the OTP makes it easier.
"Yes, it's a great default to be shared-nothing"
I'm not certain you could call elixir shared nothing. It's simply wrong; I'd look at the Elixir primitive/server called Agent which a specific construct of sharing state.
"it is not an unreasonable response to point out that there are plenty of other web servers that have similar levels of isolation"
I'm not certain you understand what the OTP is giving you over a webserver or an operating system process, it's much more about having the ability to have a message queue system baked in and easy to use that happens to be supervised and has the ability to be moved to different machines transparently.
"This is bad advocacy, and I'd really suggest that Erlangers stop trying to defend this point"
You are arguing against a straw man for me here. Maybe the original poster is a bit about this but I couldn't care less about the number of processes. I'm much more concerned that Elixir allows me to think about building better and more scalable software with a lot of edge cases solved for me. Once you get that every section of your program can be thought of a server which you can send messages to and this is super efficient, you don't need to wait for anything to block anymore it really is a better model.
"Erlang will not have some sort of unique claim to being able to run lots of such processes"
It can definitely be done in other languages but it's much harder.
"I wouldn't be surprised that nginx's isolation is more tested than Erlang itself's."
It's never been about isolation, it's about not blocking and sending messages instead. And getting supervision and robustness and fault tolerance and easy of use. Yes you could have 300 rabbit queues in front of every part of your program but I'd say it's easier and more scalable to just use Elixir/Erlang/OTP.