Hide Apache Login Popup when running CSS in unprotected area and run this CSS in protected area.

I created Wordpress website and I need help with htaccess and htpasswd.
I use htpasswd for members and somehow I should show different content (CSS) in unprotected area and in protected area. I created solution, but I need help.

I run same css style from unprotected area and in protected area by apache htpasswd.
In unprotected area this style asking to open apache login button popup and in protected area (after apache login) this style opening because it is allowed by htaccess.

Something like this:
ErrorDocument 401 default
AuthName "Members Only"
AuthType Basic
AuthUserFile /home/gdk85xikpj0q/project.tv/.htpasswd
AuthGroupFile /dev/null
<Files istyle.min.css>
Require valid-user
</Files>

I need to run this css only in protected area (when logged in by apache).
I got solution with this htaccess, but in unprotected area browser asking login and password for this file and we don't need it. I need that in unprotected area this file not running and in protected area this file should run.

Look at video. When I am not logged in by htpasswd then i always have this popup, but I don't need it and this we need to fix. But when I am logged in this css should run as it running now in video (CSS brings white background).

Please offer only if you understand and could talk about this solutions with me.