Libertarianism gives me a philosophical foundation to reason about political issues that is outside the usual partisan structure. It's also an
ideal, not a club of people wanting to gain, hold, and exert power. So you never reach a perfect world. If you want to be a libertarian, you'd better be prepared to compromise. With everybody.
Both of these attributes differ us from most political folks.
I will continue to use Nazis as an example of "a group we all hate". They've been around in the states forever and we have traditionally tolerated them. You can substitute various other groups or causes.
There is effectively no difference between having the government ban Nazis from demonstrating in the public square and Google preventing them from showing up in seach results. Sure, if there were a dozen search engines, each with 5-10% of the search market, you could make a great case that search!=visibility/speech. That argument cannot be made today, at least in the U.S. Today not only can internet giants shut you down, they can make you think you're speaking to the world when you're only speaking to yourself (hell-banning). That's all kinds of fucked up.
What's happening is that governments are effectively delegating powers of surveillance and censorship to large corporations, which gain and hold their power through government collusion. When Facebook sucks up to China to gain a foothold, claiming that any kind of openness beats nothing at all, it's not Facebook that is using China. It's China that is using Facebook. Sure, may look different to Zuck and the other cats in SV, but I can assure you that from the government side of things, they are well aware of exactly what's going on.
I think that internet companies in general made a devil's bargain back in the 90s: sure, the net is free, but in return for us tracking and recording everything you do, we'll give you even more free stuff! Who doesn't like free stuff? And it's not like when you're using the internet that you can observe how you're being tracked. As far as most people believed (and still want to believe, really), it's free stuff and there's absolutely no cost at all.
It's been a decade or two. Now the devil must have his due. Nobody cared that Google was recording your searches. But now that everybody is recording everything, it's not such a pretty world we've created.
I do not believe governments should limit corporations "just because". I do not believe we should limit the power of governments "just because". We want to limit complexity and maximize marketplace competition, whether it's in the government sector or corporate sector. That's good for everybody. In the states, the federated system we used to have allowed folks to pack up and move to another state if they didn't like their government.
So I think your question is assuming that there are two different things that I would feel differently about, government and big corporations. But these two things do not exist independently of one another. What's happening is that the role of Big Government and Big Business are becoming conflated. We are centralizing everything and creating a winner-take-all marketplace, whether it's the political parties running for office or the internet giants competing for mind-space. There are no options. There are no choices. Instead of various experiments leading to better stuff for everybody (in both government and the private sector) it's just becoming a big free-for-all for domination.
In fact, in most cases domination has already been decided. You don't think that voting Republican or Democrat is really going to change much, do you? Sure, maybe around the edges. Perhaps once every decade or two you might get a huge social program. But no matter who wins, it's the same people. The same policies. No matter whether you use Google Search or DDG, your ISP is still tracking everything. We pretend there is much more diversity and freedom of choice than there actually is.
When corporations and governments use one another to take away our choices and create society that nobody in their right mind would want to live in, something must be done. Busting up the big companies is probably the easiest, but it's honestly just half of the problem. If we could all agree on just that half, I'm a happy guy. But I doubt the players will allow us to do so.