I have used Mozilla Firefox as the web browser specifically BECAUSE it has an automatic spell checker for every text-based reply field in every web page I use.
No problems with Mozilla, nor its library, nor library-add applications. (You right-click to select the proposed corrections from the popup list.)
Haven’t ever used Opera, won’t comment.
I find spell checkers distracting at best. I like my mistakes to be my own, and as I’ve aged (and posted 200K times) I’ve been making more of them. Sometimes I just can’t remember between two spellings — often the same problem words that have been problems since I was in elementary school — and rely on the search engine, which takes a couple of seconds. :’) On the W8 machine the Chrome browser has spell check that works fine, even in the search engine boxes. :’)
That is exactly how it was for me in Opera until about a +/-week ago.