Interpreting how "political" the work was requires we keep that in mind. Saying something that most of his culture already believes isn't much of a political statement.
There is also the question of whether or not all statements are political statements. That is to say, through his fiction, was HP Lovecraft offering a political solution to the problem? Did HP Lovecraft think that the problems that he saw had a political solution at all? I fundamentally think HPL was wrestling with the fear not that his preferred political ideology would collapse, but that his 18th worldview had already collapsed and was collapsing under the weight of scientific discoveries that meant that that worldview was and always had been wrong, because it was based on a description of a world that didn't actually exist. It's within this framework I think we have to see his pronouncements, and within this framework the rise of (to his mind) mongrel races or communists was only a symptom of darker bleaker and to the educated person - inescapable truth. Scientific discovery would ultimately overturn all order, all rationality, and leave a picture of a universe which was counterintuitive to the rational ordered mind, meaning life itself and the Anglo-Saxon culture particularly could not be the rational ordered pinnacle of the universe he wished it to be.
There is a tendency in political circles and especially modern political circles to think that everything has a political solution of some sort. Indeed, there are some people for whom they feel everything is political, so that there is a very tight and one to one relationship between, "Things that are true.", and "Things which ought to be a matter of law." and perforce advocacy for taking a list of things that are true, a list of laws, and attempting to reconcile the two. And in fact, there is a school of thought which suggests this is the core of moral human behavior, and a person's ethics are revealed by how linked they see these two things and how much passion (at least) they have for this great reconciliation. It's something I see linking say socialists and libertarians - they both think that in the main, the problems they see could be fixed if only there was a reconciliation between truth and law.
To my reading, HPL wasn't making political statements. If I am correct regarding his philosophy, there could be no possible political solution any more than there could be any possible society or permanent place for humanity (particularly civilized humanity, as he saw it) once "the stars were right". He was making philosophical statements certainly, but I see no call to arms, no proscriptive formulas in his writings at all. There is racism there obviously, as there is racism in Howard (who he corresponded with), but at least in his fiction its a racism that is not easily classified according to any political system at all. HPL is in many ways reactionary even in 1776 - he opposed the Colonies revolting against the monarch. But that wasn't a normal feature of any political movement of his own day, and in other respects he has characteristics normally associated with 'liberal' ideology. HPL doesn't easily align with any block of people. He's not conforming to anything. He is fundamentally esoteric - 'wierd' to use another phrase. He's not even easily classified according to the usual divisions of his time, much less our time. What are we to make of a reactionary conservative who supports FDR and hates Woodrow Wilson, not because HPL's own political prescriptions differ markedly on much of anything from Wilson (both are aristocratic, educated, progressive on some matters, secular, racist, anglophiles), but because Wilson is in HPL's mine far too reticent in leaping to defend 'mother Britannia' from (to his mind) the mongrel barbarians that threaten it. Normal conservative politics of the day were high isolationist and busy yelling from the rooftops that Wilson was the anti-Christ for seeking against the guidance of the founding fathers to entangle the US in European wars! Nor does the atheist HPL whose best friend (so far as he had any) was a gay man easily fit into stereotypes regarding modern conservative thought.
And as I said, I don't believe that 'the right' and 'the left' actually even exist save as 'hats' for different tribes. The terms for me are far vaguer and less useful than D&D alignment (but come to think of it, I wonder if there is inverse correlation between how strongly someone believes alignment is meaningless, and how strongly they think 'left/right' is meaningful.)
Compare HPL with a contemporary political activist, say the late period writings of HG Wells, and you'll see a very marked difference in tone and style of the writing.
