Distance determination in astronomy is a quantized process. The nearest stars' distance can be determined by direct triangulation, using the earth's orbit as a baseline. Closer stellar distances are known to a higher precision because the angles are easier to measure precisely. This gives us a sample of nearby stars we can use to set up a distance-luminosity relationship, which of course must be weighted by the relationship between star luminosity and spectral class (Hertzsprung-Russel Diagram), since not all stars are intrinsically the same brightness. This in turn can be extended using other techniques.

The problem is that this procedure requires some knowledge of distance, so it is essentially a bootstrap process. At greater distances, we rely on the period-luminosity relationship of certain types of variable stars, or we use clusters which give us the constraint that all stars in them are at approximately the same distance. All of these method have some overlap, but there are also some gaps in those places where we need to use one technique to calibrate the next. This process is gradually extended out to the distant galaxies. It is also complicated by dust in the galactic plane which dims and reddens stars as a function of galactic latitude, so this must be modelled in too. Needless to say, there is a lot of informed guesswork going on. A lot of our estimates are based on assumptions made from potentially fuzzy distance determinations, so it is an iterative process. Yes astronomers are very aware of this, and they are constantly working on it and arguing about it.

In general, there is a roughly 10% error every time we jump from one method to the next, so every we time we refine one of these techniques (like the use of highly accurate trigonometric parallaxes from satellites that you point out), every value in the higher steps automatically gets improved. I don't know this for a fact, but I think Hipparchos gave us highly accurate parallaxes out to about 200 light years, not very far into the Grand Design. These results are just now filtering up to the farther distances, so we will be getting improved distances, even to the galaxies, as the research works its way up the distance domains.

This distance determination process permeates all of astronomy, and all its subfields benefit and contribute to it. It is then applied to determination not just of distance, but to the structure and evolution of heavenly bodies, which in turn helps us calibrate our distance models even better. We know our progress is genuine when independent lines of research arrive at the same conclusion from different directions. It's an incredible puzzle, and the thought that we've made as much progress as we have in just the last 150 years is an absolutely staggering achievement and a triumph of the human intellect that brings tears to my eyes every time I think about it.

Maybe you can understand why the unsubstantiated claims, blind acceptance and fuzzy logic of the anomalists pisses me off so much.