Perhaps, but the reason the western world has settled on a limited "republican" form of government rather than pure democracy is precisely so that the whims (or irrational fears) of a majority cannot trample the rights of a minority using the power of the state.
hmm...... maybe.
Yes there can be absolutely no doubt that the political leaning of world governments in democratic countries has become more "republican" (because we are both pedants and your use of quotation-marks notwithstanding, let's agree to call this "conservative" - in the true political sense, the term "republican" is more popularly linked to anti-monarch rule outside USA, I believe). However, I'm not sure that the driver for this political tilt is "irrational fear" - so I question the flow of cause-and-effect in your line of reasoning.
In my mind, the principal reason for the shift away from leftist governments is the changing profile of world communities in general, and in western democracies in particular. Since records started, the median age of the super-organism that we know as man-kind has been increasing. Maybe this has been happening because of decreasing fertility rates, or rising life expectancy, or the increasing penetration of education (which has a tendency to lower birth rates) - or a combination of all of these?
At the same time as the profile of voters is getting older, the absolute numbers of our fellow humans is increasing at a very fast rate (this may sound counter intuitive, but it isn't). Added to this is today's concerns about the ability of the earth's limited resources to satisfy the needs of a growing population
This all means that in general, citizens in the western world are becoming more risk averse and standards of acceptable community behavior when we were young are now considered intolerable in the modern era. As an example, I'm sure that like me, you were allowed to travel to and from school at an early age unaccompanied - this is certainly not a generally accepted practice in western democracies these days!
Anyhow, it's not a long-stretch in logic to extend the more risk averse nature of modern societies to what drives voter decisions on election day. Hence the tendency to more conservative governments in western democracies in the modern era - !!
Now, does the fact of conservatism (itself) enhance government's control of citizens so that "the whims (or irrational fears) of a majority cannot trample the rights of a minority"? I'm not convinced that this is a reasonable conclusion - but I remain a convertible skeptic should you have further, more compelling evidence for the claim!!
Don