-Without either a plugin or a modification to disable some of the post filters, you cannot insert adsense into the posts themselves. Period. Scripts don’t work in posts because of these filters, and there is no actual option in the admin interface to disable the problem one in particular. Yes, yes, Firefox is a bit more liberal with the way it interprets javascripts. It really shouldn’t be working in Firefox either, and the fact that it does is probably a Firefox bug.
-You can edit your theme and insert the adsense code directly. This is far preferable to putting them in the posts themselves, since you can only have three to any given page. Plus it makes your page look more professional, and it’s really not difficult to do. This is the best approach.
-There are plugins designed to do this sort of thing for you, including putting them after posts, before posts, inside posts, whatever you want. If you are not comfortable editing a theme, I recommend using one of these plugins.
-If for some weird and unusual reason, you absolutely *must* put the adsense code into the posts themselves, here’s a plugin to allow you to do that without breaking all the rest of the formatting: https://ottodestruct.com/wpstuff/scriptenabler.zip
All it does is to make the filter not apply to your javascripts inside of posts. Now, I do not recommend this. Not because it won’t work, but because it’s silly when there’s so many better ways to do it. Scripts can be tricky things sometimes, and having them inside your post body itself is not a generally good idea. But if you must, hey, who am I to say it can’t be done?