Yes, Blockfolio is safe. The app has over 6 million downloads, as well as a 4.8 star rating on the Apple App Store and a 4.4 star rating on the Google Play store.
You can use Blockfolio's portfolio tracking feature without sharing any personal information whatsoever. Furthermore, Blockfolio states in their privacy policy that they do not sell, rent, or trade any individual usage data to third parties.
On February 9, 2021, the news feed portion of the Blockfolio app was hacked to display offensive content, but the trading services were never affected. Following the hack, FTX CEO Sam Bankman-Fried reassured users that they'd be conducting a full security review of the older, non-trading related parts of Blockfolio to avoid future issues. He followed up by giving $10 to every user trading in Blockfolio (and the new ones who signed up during that week).