DDG proxies Bing results with extra privacy. Startpage proxies Google results with extra privacy (it’s a bit slow in my opinion though).

Ecosia proxies both with a bit oft extra privacy, as long as you don’t click or block the advertised results.

SearX proxies whatever you want, but its kinda slow last time I tried it.

Brave Search builds their own index, which is pretty good (on par with Bing) even though they’re only about a year old at this point. The company is a bit sketchy though.

Somehow they might got a special version of the app. Really really unlikely though, it’s probably just A/B testing or false logs.

It doesn’t require you to use Facebook though. They might use FB analytics or tracking, but probably dont, or only for very few users.

Exodus Privacy detects trackers in apps, here is their report for Ally: https://reports.exodus-privacy.eu.org/en/reports/com.ally.MobileBanking/latest/

Many other apps contain way more and worse trackers, just some Amazon and Google Firebase is on the light side.

According to Exodus Privacy (they analize mobile apps for trackers), Ally only contains Amazon and Google trackers (Google Firebase Analytics is used by almost all apps): https://reports.exodus-privacy.eu.org/en/reports/com.ally.MobileBanking/latest/

Others also say their Ally app doesn’t connect to Facebook. Maybe you have a Unicorn or a modified app (rather unlikely though)?