For anyone interested in using Sentry with Discourse, one of the maintainers of the package replied with a suggested fix.
They said that the problem was coming from Discourse’s MethodProfiler which uses alias_method. They suggested replacing that with prepend which they said was becoming more common and would allow both tools to work together.
I am not familiar enough with Ruby to understand the differences. For now, I will try commenting out this bit of code to disable Discourse’s method profiling.