How to Exclude Foreign Keys during Publish action in sqlpackage
You need to disable deployment option "Script validation for new constraints".
Foreign keys will be still created, but in not trusted state and existing data will not be validated.
Publish script will contains something like:

ALTER TABLE [Tab] WITH NOCHECK
    ADD CONSTRAINT [FK_Tab] FOREIGN KEY ([Id]) REFERENCES [Tab2] ([Id]);


This will allow you to deploy all constraints without errors, but you still need to disable them in post deployment script.