Unlike the US, Portugal doesn’t tax its citizens living in most other countries. But apparently it does tax Portuguese citizens living in certain countries deemed as tax havens!
Moreover, an individual is qualified as a resident of Portugal if he is a Portuguese national who moves his residence for tax purposes to a country, territory or region subject to a clearly more favourable tax regime included in a list approved by Ministerial Order of the member of Government responsible for the tax area, unless he proves that the change is for a valid reason, such as being seconded by his employer for performing a temporary activity.
Here is the list: https://www.pwc.pt/en/pwcinforfisco/tax-guide/2019/tax-havens.html which includes many small nations with no income tax (e.g. United Arab Emirates).
So if you plan to relocate to a tax haven country, having Portuguese citizenship could be a liability for you.
This is not an (additional) issue for US citizens, since they will already be taxed as US residents no matter where they live, so they can’t have tax residency in a tax haven.