The short answer is no, authors who self-publish are not respected in the writing world. However, the very wording of your question reveals part of the reason why not.
Your question asks about RESPECT from two groups (1) The 'writing world' and (2) 'authors'. This is indicative of the academic biased psyche of a typical aspiring writer. A 'normal' person wants financial reward over respect. The 'respect' you speak of is the same respect you sought from your school-teacher and your peers.
"Well-written" is a peer-review and rejection term it's not particularly high on a commercial publisher's agenda. The writing of Dan Brown, Stephanie Meyer, or EL James is generally considered to be awful. James Patterson is pretty terrible too . . . he doesn't even write his own books. Publisher's are 'for-profit' companies who profit on volume, they've no interest in publishing 'good books' they seek authors who's personal stories can be sold.
Once upon a time publishing was an expensive business and only publishers could publish. This enabled publishers to dictate what was published. Any author who possessed the finance to publish his own work (vanity publishing) was frowned upon - How dare he circumvent us, the gatekeepers, this work is unapproved!
I have been to third base with major publishers on more than one occasion. "Well-written" was never an issue. "We want to market this to teens so can you remove the masturbation scene." "We love this story but we are concerned about the number of children killed."
The digital era bought commercial publishers a whole new set of problems - anybody could publish at virtually no cost. Amanda Hocking was the original self-publishing queen. Sales of her ebooks reached 10,000 copies per day. The publisher's problem is that under normal circumstances an author of her standing was offered around 7% of the cover price. Hocking through self-publishing was earning 70%. It took a £2,000,000 advance to get her out of the self-publishing business.
But this story is not new. We recognise the plot from the music industry. The Internet and MP3s decimated the recording companies. Literature is just a little slow.