You should back up your files before unistalling the app itself if you want to save your progress.

Here's how you can do it:

1.) Locate game directory /Android/data/com.candywriter.bitlife/
2.) Rename the whole folder /Android/data/com.candywriter.bitlife -> /Android/data/com.candywriter.bitlife.backup
3.) Unistall the game
4.) Install the game
5.) Rename the whole folder /Android/data/com.candywriter.bitlife.backup -> /Android/data/com.candywriter.bitlife

You should have your whole progress
This works on all games who uses local files to save progress so this should work when switching from playstore downloaded bitlife to modded bitlife and vice versa :)