If they object, they can just not use it. As the article says, the petition for abolishing or reducing the fees of a license needed for Starlink was signed by 7

If they object, they can just not use it. As the article says, the petition for abolishing or reducing the fees of a license needed for Starlink was signed by 70% of the islands' population. I think that the main entity that is objecting is the current satellite ISP monopoly (that probably made a deal with the government that included protecting their monopoly as a condition of their investment).