I found a solution.
This turns off the filtering, it's working, but not a good idea...
config.allowedContent = true;
To play with a content string works fine for id, etc, but not for the class and style attributes, because you have () and {} for class and style filtering.
So my bet is for allowing any class in the editor is:
config.extraAllowedContent = '*(*)';
This allows any class and any inline style.
config.extraAllowedContent = '*(*);*{*}';
To allow only class="asdf1" and class="asdf2" for any tag:
config.extraAllowedContent = '*(asdf1,asdf2)';
(so you have to specify the classnames)
To allow only class="asdf" only for p tag:
config.extraAllowedContent = 'p(asdf)';
To allow id attribute for any tag:
config.extraAllowedContent = '*[id]';
etc etc
To allow style tag (<style type="text/css">...</style>):
config.extraAllowedContent = 'style';
To be a bit more complex:
config.extraAllowedContent = 'span;ul;li;table;td;style;*[id];*(*);*{*}';
Hope it's a better solution...