IMO I guess it depends on how you think about it. Essentially your trusting whoever is hosting the instance to not make changes to the code that would allow for tracking.

If you have the server space for it running your own is probably the most private due to less 3rd party trust. i'm sure that there are plenty of instances out there that are not publicly advertised.

but i think if you're going to use public instances either use one hosted by somebody that you at least marginally trust or i think there's a function to switch instances every few searches somewhere in the settings....