How to run part of a script with reduced privileges?

You may want to use this trick:

{ anycommand } | su -c 'tee file' user

tee(1) is POSIX utility, so you may rely on its availability.

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Or, with sudo:

{ anycommand } | sudo -u user 'tee file'

Use a subshell: (su -c 'psql -U postgres -c "<command>"' postgres) > file

Inside the subshell you can drop permissions to do your work, but output is redirected to your original shell which still has your original permissions.