To be entirely fair, some of what they're talking about does involve removing government regulations that make it easier for small shareholders of companies to make resolutions and influence the company that they own stock in. If companies want to change the rules about who can ask for changes and what sort of changes they can ask for, I don't think I care all that much.
Where things get a bit stranger is where the editorial starts talking about how index funds often own more stock than other stockholders, and that this gives their managers and proxies power to introduce resolutions and changes but doesn't require them to listen to the investors that are actually paying for the fund to have all that stock. This, apparently, means that some of those funds might start acting in ways that are more in line with the whims or specific interests of those managers and proxies rather than the investors themselves. Given my liberal distrust for the notion that capitalism always produces the best result for the individual consumer, this comes as absolutely no surprise to me, although somehow it's only apparent to the writers of this editorial once those whims and interests line up with liberal talking points instead of conservative interests.
What I don't understand, then, is how a proper small-government conservative or libertarian is supposed to justify government rules that would limit how fund managers would use that influence. As I understand their position regarding the free market, if I don't like the way a trading company is managing my money, the proper recourse is to find a different one, not have the government make a rule about exactly what benefits the trading company in question is allowed to ask for. Of course, I don't mind the idea of the government creating such rules, but then, I'd also define what is in the investors' best interest somewhat more broadly than this editorial wants to.
In the end, this editorial just seems to be annoyed that some investors have the power to force companies to manage their people and operations in a specific way. Unfortunately for them, the only way to stop that is a government powerful enough to make rules about how investors and trading companies can use their money, and I don't think they'll like that precedent any more than they like the current state of affairs.