Just curious, if so many people buy index funds, then the largest direct shareholders of those S&P 500 companies have to be these firms (e.g. BlackRock, Vanguard, State Street, Invesco and Charles Schwab). Does it mean they can basically decide everything determined by shareholder votes? Are there different voting rules between institutional shareholders and individual shareholders?
Yes, in theory, index ETF providers CAN decide CEO of a company, or anything else that a shareholder vote would determine, since they are allowed to vote those shares.
For example, you mentioned Blackrock. As per the Responsible Investiemnt FAQ:
Blackrock excercises proxy votes in companies. This means any vote on a proposal to replace the CEO, can be voted by Blackrock.
Blackrock has dedicated Blackrock Investment Stewardship team for this
FAQ#8 states that the team engages with invested companies directly, not only via proxy votes.
While it doesn't state so outright in FAQ, in theory, as shareholder, the company can introduce votes it wants at shareholder meetings like any other equity holder.
So, the answer is "Yes, index ETF providers can do anything any other investor does" as far as corporate governance, except they may be far more effective since they have dedicated professional teams dealing with this AND the clout.
As far as "different voting rules", it's nuanced. Some companies have multiple classes of shares, with different voting rights (as Ceejayoz's comment noted, Facbook is (in)famous for this). But again, in this, there is no difference between index ETF providers and an individual investor buying same share class on open market.
Not only can they, but apparently they do.
Research by Gormley and Keim, as detailed here, found
Firms with more passive ownership had more shareholder-friendly governance, indicating that passive investors do pressure firms effectively. The largest effect was the 9% increase in independent directors associated with the 10% increase in passive ownership. In addition, a one percentage point increase in passive ownership produced a 0.5% increase in the likelihood of removing a poison pill and reducing restrictions on shareholders’ right to call a special board meeting. While these may sound like modest numbers, they are significant because, overall, only about 4% of firms remove a poison pill each year, while just 0.7% ease restrictions on calling special meetings.
“Our evidence suggests that a key mechanism by which passive investors exert their influence is through the power of their large voting blocks,” the researchers write. A 10% increase in passive ownership is associated with a 4% decline in support for management proposals and a 10% increase in support for proposals considered shareholder friendly.