Are you on the latest staging? I cant replicate this

commit 1746f5798b0b71c7b32ae1350d70fff18d8ff228
Author: Allon Moritz <allon.moritz@digital-peak.com>
Date:   Thu Feb 23 11:39:44 2017 +0100

    Remove home option in media form field (#13893)

double checked on staging and still cant replicate

Are you trying the frontend or the admin console?

joomla-cms/staging@d7caa77

As the opening statement states:

Steps to reproduce the issue

Go to front end and edit article - click select on the media field

Its fine in admin, and broken in the frontend.

Can't reproduce that as well. Dropdown folder appears as expected in frontend article edit. Even without first saving the plugin parameters.

I am unable to reproduce too. Your 1st screenshot is different than in RC4. For the Directory field, it should have a dropdown with an - Use Default - option. Have you done a clean install of RC4 downloaded from:
Joomla!

Tested again on Chrome and Edge on Windows XAMPP, can't reproduce that behavior even after opening and closing the modal multiple times.
I noticed a 404 error in the console about the ajax-loader.gif, but should not be related (imho).
So it may be related to Mac somehow?

See the source code, the "normal" has options, but the "chosen" js widget has no options, so this looks to be the implementation of the chosen dropdowns, or something along those lines. EDIT: uploaded larger html screenshot

width: 2px; . WTF!!!

upstream bug confirmed. harvesthq/chosen#2029

Putting this:

.chosen-container .chosen-choices .search-field:only-child,
.chosen-container .chosen-choices .search-field:only-child input {
    width: 100% !important;
}

into the templates css fixes the problem for me like harvesthq/chosen#2029 (comment) states

@PhilETaylor the sooner Joomla goes away from chosen the better: harvesthq/chosen#1740 (comment)

hmm can somone on a Mac try to confirm this? I have tryed this now multible times. But i can not reproduce the problem on Windows using the last version of chrome.

If I load http://127.0.0.1:8000/index.php/index.php?option=com_media&view=images&tmpl=component&asset=61&author=16&fieldid=jform_com_fields_somemedia&ismoo=0&folder= directly in the browser it works fine - the width is fine

Its only when that url is loaded as an iframe source in a modal on the frontend that I can replicate the upstream issue

Can't confirm:
Difference in Screenshot of opened Comment is Directory:

So is looks fine in Modal:

System information

3.7.0-rc4
macOS Sierra, 10.12.4
Firefox 53 (64-bit)

MAMP 4.1.1

• PHP 7.0.15
• MySQLi 5.6.35

The same modal is used when you click the image button in TinyMCE when editing a content item on the front of the site - this ALWAYS displays the folder list correct.

This further leads me to believe that this is a com_fields initialisation of the modal that is at fault

If you want to have a look at the respective com_fields specific code for that formfield: https://github.com/joomla/joomla-cms/blob/staging/plugins/fields/media/media.php

It's the exact same code in front- and backend. I honestly can't think of a place within the PHP code of fields which could generate your issues. It should be the same behavior everytime anyway.

@Bakual as the comments above prove - it is an issue - and is caused by upstream bugs in chosen...

I never said it's not an issue. It's just that com_fields doesn't do anything different here than com_content does. It's the same formfield that gets rendered and it's also the same code in JForm which does it. There is no difference here.
Thus I wonder where the issue cos from, as I don't think it's a com_fields specific one.