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perl -i -p -e 's/Pridetree/Bridetree/;' /Applications/Sourcetree.app/Contents/Resources/Assets.car
You can also use the program ThemeEngine to modify the Assets.car file in Sourcetree - or any Mac application for that matter - to change any graphic in the application (as long as it's in the car file).
ThemeEngine may not work on newest versions of OS X though :(
You are correct in that ThemeEngine does not work on Catalina 10.15.
Thank you @Sterling Bourne ! It worked, but I had to use sudo.
Dear Atlassian please keep the pride support to yourselves, don't force us to watch it everyday! Thanks.