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These two addresses are the only computers in the world that have both the "https"//" Certificate/Key for the name "auth.yale.edu" and also the Certificate/Key to digitally sign messages in a way that other applications will trust that the message came from the Yale Shibboleth server, so using any other address here will not work.
In Windows: Copy, Edit, Copy Back
In Windows, the "hosts" file can generally not be correctly changed in place using a text editor. There are a number of system protections here, and when the editor tries to save the new file, the data is rerouted to a new file in some other location where it does no good. You should copy it to another directory, edit it in the other directory, and then copy it back.
Testing
It is generally a good idea to make two copies of the "hosts" file to two subdirectories, which I will call "saved" and "test" . Edit "test\hosts" to add the one line with "128.36.64.90 auth.yale.edu". To copy "test\hosts" to "C:\windows\system32\drivers\etc" (or to copy test/hosts to "/etc") you need administrative (or root) privileges. On Windows, simply copy and paste or drag and drop the file from test\hosts to C:\windows\system32\drivers\etc. First you will be asked if you want to replace the old file. Then you will be asked to approve the use of administrative privilege to change a system directory.
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