Hello -
View All Site content is an application page. You can tell this because its URL includes "/_layouts" in the address bar. So when a user selects View All Site Content, the user is sees an application page which inherited its look and feel from the master page titled application.master.
It's recommended not to modify the application master page. However, if you choose to do so, definitely create a backup copy.
Here are your options:
If you tie your brand styles only to your custom master page, when the user goes to any of the application pages, the look and feel will revert back to the out of the box styles and you won't have the issue of the page displaying a particular style which may not look well with the rest of the page.
The other option is to use a theme. Themes can affect the look and feel across application pages, site pages, and system pages.
If I'm designing a site and I know upfront that it's important to carry accross the custom look and feel throughout admin pages, I'll put all or most all of the custom styles in a custom theme to achieve the look I'm going for.
Where did you originally put your styles at? Was it in a separate file referenced from the master page? Or did you use a theme to begin with?
In summary, the "cleanest" thing to do would be to create a new theme versus using an existing theme to make your changes to. If you create a new theme, then you could literally only include the styles you need specifically for Site Actions (only a line or two) in the theme.css file (since that's the only style that you need to override). Or you could put all of the your top navigation styles (red bar with white font) in the theme file so that the look and feel is carried accross the entire site.
If you decide to create the custom theme, let me know if you need help. It's really super easy to do!
- Celina