Policing ideological speech: Laws against incitement. Fact: There are also laws about curbing private monopoly control of certain kinds of media in a given area.
Government complaining about bias: Civil rights laws. Equal Opportunity Employment.
When the actions of both powerful government organizations and powerful companies start to infringe on the speech of constituents, then the representatives elected to that government have taken action in the past.
Google could in principle make its results insanely left-leaning and the first amendment should protect them.
This has already happened. I don't think the first amendment would necessarily protect them. There is already a precedent for government to curb monopoly power in media.
They must be very careful not to let the narrative become "we don't bias our results, we swear!"
If "they" is Google, then the bird has already flown the coop in this case.
Their position should be a very firm "don't tell us what to fcking do."*
Should other companies start saying the same? Maybe having far less government would be far better across the board. When one concentrates power, someone figures out a way to abuse it. This applies as much to Google as it does to government.
EDIT: No such thing as "Hate speech laws."