Under specific circumstances, yeah.

Wouldn't that seem to violate the idea of freedom of speech? What if someone running for public office requests that I "forget" and not share what I know about some bad things they did in the past?

Perhaps it would, but there are plenty of other restrictions on freedom of speech. And this particular law does not apply to news media etc, as far as I understand - just search engines and similar databases.

Sure, of course there are and should be reasonable restrictions (shouting fire in a crowded theater causing immediate danger, for example). But is this a restriction that society should accept? How could you expect to have a functioning democracy if a politician could make people "forget" to stop them from sharing any inconvenient facts about the politician's past actions?

And perhaps I want to make a list of sources where you can search for information about politicians to hold them accountable. If it's not censorship for them to be able to stop me from linking to true things they don't want people to see about them, then what is?

This law has been used to disappear search results from newspaper site search engines.

If it can't be found by anyone, isn't that about the same as deleting it?

Europeans don't necessarily have "freedom of speech". Not in the same ways Americans see it.

Europeans overestimate the benevolence of their governing bodies. Things that limit freedoms of people are the same as things that empower government

The way I see it, this European law is already quite dangerous and will become more so as tech merges with our brains. People might wake up one day having 'forgotten,' for example that Trump grabbed someone by the pussy, because some court decided so. Similar to how users saw copies of the book 1984 disappear from their Kindles not long ago because Amazon felt like it.

If these specific circumstances are NDAs, classified government information and such, that is completely okay because they require a knowingly signed contract violation of which leads to fines and charges. The problem with RTBF is that there's no such contract, or rather it's implicit.