So I found a fix for the issue: I increased the buffer size on the server. This was the full error text:
2018/04/17 02:23:24 [error] 54028#54028: *29421 upstream sent too big header while reading response header from upstream, client: [IP REDACTED], server: [REDACTED], request: “POST /?wc-ajax=add_to_cart HTTP/1.1”, upstream: “fastcgi://unix:/run/php/php7.0-fpm.sock:”, host:[REDACTED], referrer: [REDACTED].
However, is this potentially an issue? e.g. are the headers sent actually bigger than they should be?