You'd have to trust whatever host, but if the actual server was handled by the right reputable organization, anonymizing information should be relatively easy (if and probably only if you had a sufficiently sized user base). You basically would just have chunk up the data when you send it, fuzz time on the order of a minute or five, and make sure it didn't have any ID attached to it in any public data sets.

With a smaller user base, you could maybe make deanonymization significantly less valuable/harmful by allowing users to set dead zones locally that they don't share data from. So maybe in a city you set 2 miles from your apartment and in a more urban area you set 5, and the same for your place of work or other areas that you consider potentially invasive to a bad actor. A small base would likely still allow your route to be correlated, but removing enough of the ends cuts the risk down a lot in theory.

It's something you'd have to stay cognizant of, but it might be able to be done in a privacy protecting way.