Why are US equity prices and inflation inversely correlated? Many comments on this r/stockmarket Reddit thread hypothesize an inverse correlation between USD value and US equity prices. Why would this be true in theory?

It's not true in reality, right? Has the correlation of inflation and stock prices changed in the United States over the last two centuries? - ScienceDirect



Abstract
The relationship between stock prices and the inflation can be either negative or positive, depending on the strengths of various theoretical channels at work. In this study, we examine the dynamic conditional correlations of stock prices and inflation in the United States over the period of 1791–2015 under a time-varying framework. The results of our empirical analysis reveal that correlations between the inflation and stock prices in the United States evolve heterogeneously overtime. In particular, the correlations are significantly positive in the 1840s, 1860s, 1930s and 2011, and significantly negative otherwise. The policy implications of these findings are then discussed.
The price of a stock is the discounted value of its future expected payments. The rate for discounting includes inflation. If nothing else related to the stock except the expected inflation rate changed, the discount rate would increase, driving down the price of the stock. That's a theoretical/mechanical reason why prices might drop due to a change in inflation and only inflation.
But inflation doesn't tend to happen all by itself. It accompanies other macroeconomic changes.
If inflation is happening because of economic problems, such as a shortage of materials or trade problems driving up prices, then we might expect the cash flows to decrease at the same time as the discount rate increases.
If prices are moving up in a perfectly orderly and expected way and not because of economic problems, then we could imagine both the cash flows (numerator) and discount rate (denominator) increasing in such a way that they offset each other. In other words, the numeraire could be irrelevant.
If inflation is driven by increased demand, we might expect the cash flows to increase faster than the discount rate, leading to a rise in stock prices. And of course, there's also the mechanical relationship between today's inflation and prices. If suddenly a dollar is worth a lot less, you might expect everything to increase in price, including stocks.
Many aspects of macroeconomics are too complex or unstable to reduce to a few rules of thumb. Macro models help us understand what happens in a fairly specific set of circumstances. More specific than &quot;inflation of unknown origin.&quot; Based on the wording of your question, it seems like you have a reasonable handle on this fact. You are correct in thinking that the relationship between inflation and stock prices is not reliably in one direction.