I have little time for Trump but I do find the idea that the democratically elected head of state of one of our closest allies might not be invited because some people wish to stop it, uncomfortable.
The issue isn't that he hasn't been invited - he has for both state and working visits. The point is that (on this occasion) he has declined to visit, and in the case of the state visit he has kicked it into the long grass.
But on the broader point - certainly for state visits - it is for our country to decide whether, or not, to extend an invite and that should be done sensitively with reference to public opinion. So should the Head of State choose not to extend an invite due to public opinion, so be it (although I think this is pretty unlikely to happen). Moreover, in a democracy that respects freedom of speech it is perfectly reasonable for people to oppose any visit and demonstrate robustly against (within the law) if a controversial leader is invited and comes.
So it actually looks more like Trump is snubbing the UK, rather than the UK is snubbing Trump.
It speaks volumes for our supposed 'special relationship', that Trump has already visits virtually all of his 'key allies' (Germany, France, Italy, Japan, Israel, South Korea, Saudi Arabia, Belgium etc) plus other major powers, most notably China, but hasn't visited the UK.