Not quite. That link is doing something weird and including the corporate tax rates to arrive at "total" tax rates. The median total of individual and payroll tax rates by those tables was 16% in 1979 and 11.4% in 2019. But even that isn't right because it apparently isn't counting the so-called "employer contribution" of FICA for people who aren't self-employed:

https://www.ssa.gov/oact/progdata/taxRates.html

Using those numbers for the payroll tax rates, the median combined rate was 19.66% in 1979 and 17.7% in 2019. And this is slightly overestimating the rate in 1979 because the self-employed payroll tax was less than the combined employer+employee rate in 1979. So there hasn't been a significant reduction in 40 years, and the rate on small businesses has increased by several percent.

But that's not all. The start of that table was a high point. The median effective tax rate in 1950 was 5.5%:

https://www.irs.gov/pub/irs-soi/80inintravmatr.pdf

That probably doesn't include FICA, but FICA in 1950 was only 1.5%/3% (and again less than the combined rate for self-employed back then), so the median federal effective tax rate would have been <8.5% in 1950 compared to 17.7% in 2019. And 1950 isn't even the low point, it's just the earliest number in that document.

The federal government dramatically raised taxes on the middle class in the early to mid 20th century and they've been stuck there since.

Presumably it’s including the average incidence of corporate rates because some small fraction of earners in the middle quintile pay those rates as business owners.

I happen to agree with you about who’s “really” paying for employer FICA, but there are many other taxes not directly assessed on the middle class that they’re likely paying for anyway. You can’t just tack on the full rate; not everyone in the middle class is paying FICA on every dollar of their income, there are many middle-class retirees.

Yes, the government is much, much larger than it was 75 years ago, and some of the burden for paying that has fallen on the middle class.

But the fact remains: Every major tax reform package from Reagan to Bush II to Obama to Trump has either lowered middle class rates, increased middle class deductions, or made significant new credits available to the middle class. Usually more than one of these.