No the adapters aren't specific to IE6. The adapters cause the ASP.NET framework to render alternative markup (better markup, hopefully) for menus, tree views, etc. They are set up (in the .browser file) to do that alternative HTML generation for all browsers, not just IE6.
However, if you are having problems with IE6 then, typically, it is because you haven't sufficiently "prepared" your pages to deal with IE6 when the adapters are in play.
To understand that statement, you need to do a couple of things. First, re-read the instructions provided in the white paper, http://www.asp.net/cssadapters/whitepaper.aspx#SamplesUsingInYourWebSite. Make certain that your pages have properly set up the <link> tags that these instructions mentioned. Pay particular attention to the paths that you use for the style sheets, etc. to be sure that these files actually exist on your site. Notice, too, that there is a conditional comment that pertains specifically to IE6. Sometimes people mess that up and then their pages don't render in IE6 when they use the adapters.
If you are still having problems, then you should search these forums for other postings wherein people using the adapters had problems with IE6. Most or many of those postings will include (ultimately) the resolution to the original problem. Perhaps you are running into the same problem that someone else has... and can solve it the same way.
To search these forums for this sort of information, try using the search box above with:
sectionid:1018 AND ie6
The sectionid:1018 tells the search to restrict its results to messages posted in the CSS Friendly Adapters forum. This will narrow your results to just what you really need: discussions about how others who are using these adapters have overcome problems specific to IE6.
Hope this helps... and I'm glad you are enjoying the adapters. Best regards,