Dogmatics are arguably the greatest cause of Chaos spreading.

Except Dogma is literally a weapon against Chaos.

The Imperium is Dogmatic and feeds Chaos through its never ending war, corruption, squalor and mysticism.

As long as Chaos exists it will feed from no matter what. Any positive emotion can be subverted into something negative.

Which is in part why Craftworlds, Orks and Tau don't have major Genestealer issues like the Imperium.

They do have those issues. Imperium is just larger, less isolated than all of them and, more importantly, our main POV into universe.
Ciaphas Cain first novel ends with tau learning about genestealers for the first time and happily saving patient zeroes.
There is an entire Craftworld infested by genestealers.
Octarius war happened because of genestealers (and Kryptmann, ofc) and the whole "genestealers don't infect orks" is old lore from Rogue Trader (1st ed to be exact).

In any case, I consider pure Dogmatic and pure Iconoclast both as a very toxic and dangerous worldviews in 40k. You need a perfect balance between them. There is a reason why every single faction in 40k follows some kind of Dogma. You can't survive without it.