This cannot be done in InDesign.
You can do this in Acrobat Pro, assuming that the PDF readers the users are using are either Adobe Reader or Adobe Acrobat. With very old versions this may not be possible.
For older versions Reader versions (earlier than Reader XI), you'll need to enable the feature. The location of the command varies somewhat with the Acrobat version. For example, in Acrobat XI, you would choose File > Save as Other > Reader Extended PDF > Enable Commenting and Measuring.
The ability to Export PDFs directly out of InDesign with Enable Commenting already turned on for Reader would make a great feature.
Please add this as a feature request at the following link: Feature Request/Bug Report Form
From what I'm now hearing, in the latest version of Acrobat Reader, Commenting is turned on by default. I do not have Reader to test this. So you may want to download the latest version of Reader to check it out.
I don’t remember the last time I had to enable commenting but it was quite a few years ago.
I guess it would be a good time to tell all of my clients to upgrade to the latest Acrobat Reader.
I want to say it started with Acrobat/Reader 9 but it would be a guess.
It started with Reader XI and continues with Reader DC.