I would like to access other users public data to show in my website when they configure the page by their username/id. It means I will create an app on FB/Instagram side and with the help of this app's access token I would like to fetch public data of other user.
Is this scenario valid now? Earlier it was possible but I am not sure now with changes in policies. Even the documents are not clear enough which can say it's possible or not?
Has anyone tried this out recently?
Users: Only data of users who specifically authorized your App is available, depending on the authorized permissions. It does not matter if data of user profiles is public or not, you have to get permission from each user separately.
Pages: If you want to get data of pages you don´t own, you have to go through a review process with your App to get access to "Page Public Content": https://developers.facebook.com/docs/apps/review/feature/#reference-PAGES_ACCESS
That´s for Facebook, about Instagram you can just hit the docs (as well): https://developers.facebook.com/docs/instagram-api/business-discovery
My number one recommendation, in this case, is Facebook API or Instagram API from Data365. I may be considered biased since it is the tool I work for, but it is really a reliable tool you can get public profile data by users ID or username. Of course, you can use the official Facebook/Instagram APIs for searching all public objects (post, user, page, event, group, place, check-in). But note, the official API has a number of restrictions. Andyrandy has already described them in his answer. Compared with official APIs, we do not have such restrictions. Besides, our APIs provide such unique features as gender and age recognition (via face photos) along with identification of post reactions that give a competitive advantage in obtained analytics. Data365 APIs also enable developers to create monitoring tasks for a one-time or auto data update. And above all, we do not break the law but only provide web scraping within the legal framework.
