The aprs.fi passwords can not be used when logging in to the APRS-IS servers. aprs.fi and APRS-IS are two different things.
The APRS-IS network consists of roughly a hundred servers distributed around the world, run by a large team of volunteer server operators. APRS-IS requires the use of the passcode number for logging in and sending data to the APRS-IS network. APRSdroid and most other APRS applications connect to the APRS-IS for sending and receiving APRS data. APRSdroid simply gives your passcode to an APRS-IS server when logging in. The passcode is a static number calculated from the callsign, and it cannot be changed.
If you're using APRSdroid, you can get a passcode from the APRSdroid team. It may take a short while for them to respond, as explained on the FAQ.
Some APRS-IS servers also accept TLS/SSL connections, as an experimental feature, in which case you can use an amateur radio certificate, together with your private RSA key, to log in. The TQSL app can be used to request such a certificate from the ARRL Logbook Of The World.
aprs.fi is a web site, which connects to the APRS-IS network just like APRSdroid itself does, collects APRS data, and stores it in a large database. aprs.fi has its own user database, with usernames and passwords. Each aprs.fi user may choose their own password, and it can also be changed afterwards.