I too find the gender rift in the study really surprising. I wouldn't immediately draw the conclusion from it that Czech Republic has become more socially regressive than in the past. My feeling is the opposite when it comes to how many women I see in managerial, political etc roles. Although there is still a lot of improvement to be made. Not to rely solely on my feelings i did pull up the newest Gender Gap index which is available here: https://reports.weforum.org/docs/WEF_GGGR_2025.pdf
The index is calculated for individual countries which enables to compare the Czech Republic to China for example. I did this out of curiosity and funnily enough - we have the same exact index down to the decimal. So both china and Czech Republic have a lot of progress to do. The entire study is pretty detailed and allow for comparison in various sectors such as income, education, health etc. One interesting aspect I did notice in the European region is that eastern European (read ex-communist) countries, tend to have a lower index. But enough about gender parity.
The educational aspect of popularity of the communist regime you are mentioning could be explained by a lot of factors. From a blunt "Only uneducated people think communism is a god idea." to a more economical approach such as "People with lower incomes tend to prefer regimes that re-distribute wealth in a significant way". That seems logical and doesn't surprise me at all.
But we really don't throw people under the bus. There are differences in income, privilege, education, etc. The society isn't homogenous and never will be. But these differences aren't extreme compared to countries with "true" capitalism.
What we have here probably isn't the "capitalism" you have in mind. It is a democracy with a mostly free-market, with some regulations and checks, some subsidies, somewhat progressive taxation, free healthcare and education for everyone. There is a decent social security "net" as we call it too. It's actually not bad at all.
As you mention capitalism I would like to declare that I in no means want to defend unchecked capitalism such as we see it in the US. I believe this extreme example is the reason why many people tend to find communism - the other extreme - so attractive. Turns out moderation is key, who would have thought?