Populism may well have become a slur these days, however it encompasses a vast swathe of politics, both left and right. The SNP might not like the association with Trump, yet their indy ref was a precursor to what occurred in 2016. They are not particularly keen on the Brexit comparison either, despite some important similarities. For as with exiting the EU, any withdrawal from the UK is going to require the acceptance of economic turbulence. Instead of getting their hackles up over unwelcome bedfellows, the SNP should simply have frame Khan as the distant, unchanging establishment. Admittedly, this grows more difficult the longer they are i power (they being the Scottish establishment for all intents and purposes).
Like as not, there probably is a section of the nationalist base which is anti-English. Suggestions that it is broadly representative is where the issue arises. Sadly, conflating extremes is all too easy crutch for those in a position of control. IIRC, Khan resorted to something similar during the BBC's EU debate.
None of this does Dugdale any favours of course, who is in enough of a struggle as it is.
An example of the authoritarian policies to which i earlier referred, would be that state appointed guardians which drew so much controversy.
Populism can obviously have a broad definition and can encompass a wide range of identities and ideologies but if we're labeling the SNP as populist then Labour could be seen as such with Corbyn in charge, and even the Tories' approach to Brexit could be seen as mildly populist. Most parties have an element of populism, or at the very least a populist faction, but the direct comparison between the supposed division of the SNP and the division of someone like Trump is a bit laughable and quite ridiculous. As you say the SNP have long been the Scottish establishment now...and policy wise they're a very uncontroversial, if arguably bland party.
Scottish Labour still like to play the referendum up as some divisive event that's fractured a nation but the reality is fairly different; for all the fairly blinkered Yes supporters who will rant against anyone who disagrees with them and insult such people, there are much, much more who have sort of moved on from the whole thing fairly comfortably, and continue to hold your views without forcing them on others.
I've never fallen out with people I disagreed with over independence, and I've not seen anyone else really find themselves doing so either, bar the occasional heated discussion...which kind of comes with the territory of politics.
And again while there may be some fringe elements of the SNP who demonstrate anti-English sentiment it's really not prevalent. At all. The SNP held the 2014 referendum on the basis of people
in Scotland voting...and never really displayed any sentiment against the high number of English people who live here. Again, you'll find plenty of tiresome people on Twitter, but it's not broadly representative of a party which has over 100,000 members.
The SNP do have a little bit of an authoritarian streak, although it's still relatively limited and nowhere near the scale of May's Tories with plans like the Snoopers Charter. The named persons scheme was largely a case of something being inflated to epic proportions when it was, again, a relatively bland and basic policy.
https://www.reddit.com/r/Scotland/comments/4idu4i/the_named_person_scheme_what_it_will_do_and_what/
There might be a tad of bias in that but it seems like a reasonable summary of what the policy was supposed to be, and why the reaction to it was a bit over the top. I'd have the OBA down as a better example of an authoritarian policy...although again that's more down to its framing than the intent behind it.