This is an interesting intersection. It either implies that all employers are left-aligned (not true) and therefore willing to fire employees that hold right-leaning opinions, OR that low level employees are so expendable that it literally any reason can get them fired if enough people complain.
I don't ascribe a right or left bias to them. It's the mob that has the bias (perhaps because of age or ideology or certainty or something else) and the mob uses the technology and then the HR department responds by firing the employee.
Do we need to coin the term "DDoE"? Distributed Denial of Employment. It's a hack against the socio-political system that targets find themselves in, not too dissimilar to Swatting.
It has more to do with aggregate action, which has recently been made possible with platforms like Twitter, than with the particular ideological stances.
My personal experience is a lot of HR departments do have a left-of-center bias to them, especially at the lower-levels (but at times reaching all the way to the top). A few reasons:
1) HR departments tend to skew female, and women on average skew somewhat more left-of-center than men do
2) They often have special teams for "diversity & inclusion", which inevitably tend to be filled with people with left-of-center political views
3) They'll put requirements like "commitment to diversity & inclusion" in job descriptions, which can (ironically) act as a filter to remove political diversity. Those phrases can get copy-and-pasted into job descriptions in other departments too, but while for many in engineering/sales/etc it is just compliance boilerplate with little real significance to the hiring process, HR really means it.
Of course this isn't universally true, I'm sure there are some HR departments out there full of Trump supporters. But most of the people here would not be working for those kinds of companies.
But I doubt they will care until a conservative employer fires someone for tweeting support for a progressive belief.
It's mostly this. When you're a small-medium business, the last thing you want is negative PR and people canceling or DDOSing you because one of your employees wrongthinked.