The parallax calculations depend on the baseline,
so it depends on how you take your baseline. The use of photographic plates and keeping precise records on time, location, and orientation of the telescope has allowed us to extend the baseline a fair piece. Not only can we get the AU as a baseline, but because we can approximate the sun's orbit around the center of the galaxy, we can extend the baseline beyond an AU.
That does still limit to relatively close stars, but from there you can start to work with relative/absolute magnitude to determine the distance to the star. The initial work there was done with binary pairs where you have an independent means of determining mass. But once that is established you work more with red-shifting. It all keeps feeding back on itself, but you get further and further away and become more and more comfortable that you assumptions and calculations are correct.