Last I checked Stock Market it open to all for trading and investing. This is another article that has twisted the facts to basically hating on Donald Trump's success so far.
Sure, let's repeal Obamacare and tell the poor to invest in the stock market to get enough money to get medical treatment, I'm sure that's gonna work out great for them.
Stocks and most other financial instruments will - on average - not give meaningful returns over the timespans that sigificantly would alter social mobility if you can't invest significant amounts of money, or have insider information of questionable legality.
Anything that significantly can alter social mobility must affect early life. Things like giving access to better education for your children, or living in neighbourhoods and circumstances that give access to better contacts and networks can affect social mobility, as can other more context related factors. Since stock markets only give relatively high returns over several decades, as it is quite volatile over shorter periods of time, it's not a reliable source of social mobility.
So while financial markets can improve your pension and retirement, effects on the much more important social mobility metrics is rather tenuous, except in very rare cases.