EDIT: it may be worthwhile for those interested in answering this question to familiarize themselves with the OP's earlier posts throughout the stackexchange site - e.g. here (now deleted), here, or here - under this and related usernames. I did not check the username ahead of time, or I would not have answered; that said, I've decided to leave this answer up since it may be useful for other readers.
Re: my decision to vote to close after answering while not deleting my own answer, see this meta discussion.
No, it's not.
(Unless you interpret "logically incoherent" with "incompatible with my own intuitions about sets," which is - to put it mildly - questionable).
First of all, the claim that regularity in ZF resolves Russell's paradox is a (very common) mistake. Adding an axiom never removes inconsistencies; any contradiction present in the weaker system remains present in the stronger system. Rather, what saves ZF from Russell's paradox is the removal of full comprehension - mere separation only lets us prove that for every set A the set R_A:={x in A: x not in x} exists, but that's no paradox at all (the Russell argument shows that R_A is not an element of A, but so what?).
What the axiom of regularity does is imply that the class of non-self-containing sets is the entire universe. But that's a separate issue.
More substantively, there are set theories which permit (indeed, require) self-containing sets which are known to be consistent relative to theories we have high degrees of faith in. For example, the theory ZFC - Regularity + Aczel's antifoundation axiom is consistent if ZFC is, and proves the existence of self-containing sets.
For more dramatic examples see e.g. this article of Holmes, especially section 6.2 - the point is that there are set theories which imply the existence of self-containing sets with extremely weak consistency strength.
And in a more normative direction, various authors have actively argued for such theories; it may be worth reading their arguments (see e.g. the sources in the Stanford Encyclopedia article).
All that you've argued is that self-containing sets contradict one particular intuition about sets. But nobody has a monopoly on that notion. Unless you interpret "logically incoherent" as "in contrast with my own beliefs," there's no issue here.