First off, these are tweets - they're easy to misinterpret, and they require context. As I've listened to, and read from "the 4 horsemen" atheists over the years, one consistent theme has been to contrast dogma against evidence. You can do a lot of good analysis using that simple contrast.
From that perspective, it's easy to see how Stalinism, Nazism, Islam (and Christianity BTW), all fall into the dogma-based side of analysis. In that way, it's not unreasonable to lump them - albeit crudely - into the "religion" bucket.
I agree in the sense that religions are simply another kind of ideology, therefore some religious ideologies share much in common with religious ideologies - Stalinism, nationalism, Naziism. No problem with this view at all.
Millenarian ideologies are clearly the worst, be they Islamism, Communism or Naziism, as they strive for a perfect society, almost anything can be justified. "What violence would you not commit to exterminate violence?"
Looking back at history will show us that millenarian movements are a recurring feature of human life [The pursuit of the millennium - Norman Cohn and The Bullet's Song by William Pfaff are really interesting on this topic. Highly recommended]
In this case, based on the evidence, we have to say that human society will
always be prone to such ideologies when the 'right' societal conditions appear.
On to dogma, I'll define this as meaning holding something which is not objectively true to be incontrovertible. You would have to say that Dawkins also holds some dogmatic beliefs. For example, he holds that we have a responsibility towards humanity [a religious concept]. In addition, I cannot see him ever accepting that holding a false belief can be anything other than bad i.e. religion. He dogmatically holds the belief that truth is
always important [whereas there is no objective reason to think that holding a false but beneficial belief should be corrected, if it results in purely negative effects].
Now not all such beliefs are equal of course, but beliefs are based in evidence or they are not. And many of his beliefs, even if not dogmatic, are not based in evidence.
As you noted, secular ideologies can be millenarian too, and there is some evidence that secular millenarian ideologies are the most murderous [although small sample, historical circumstances, etc could have skewed this].
This all has to be put into context of Dawkins' belief that religion in intrinsically harmful and every effort should be made to purge it from society. This logic only works if he assumes that it would be replaced with something 'better' - i.e. Dawkins' secular humanism. Again, he has no evidence to believe this will be the case.
Humans make meaning through myths [stories about the nature of the world which aren't objectively true] - humanist myths, nationalist myths, communist myths, religious myths, etc. One thing is certain, there will always be a diversity of myths in the world.
Some will be benign, others malignant. If society managed to destroy benign and moderate religious beliefs, it might well create a fertile breeding ground for malignant new ones. A radical break from the past with its unsettling and dislocating effects has a reasonable, but ultimately unknowable chance of this.
If all he focussed on was fanaticism then there wouldn't be a problem, but he finds fault with people who hold benign views also simply because they are not 'true'. I still fail to see how he can decide that his views are 'true' by any objective standard though. He ultimately shares the same failings as universal monotheists, that given the correct 'education' everybody can see the light and achieve 'salvation' [freedom from violence an irrationality]. To see the world this way though requires avoiding certain apparent truths about human nature and society. Collectively, we are violent and irrational.
. Whether I'm respected or not on the forum depends on my posts and readers' interpretation of them. What Dawkins writes, tweets, says likewise can affect the respect in which he is held.
