I find it particularly concerning regarding the military. The President is Commander in Chief, and thus any orders he gives or attempts to give to the military would be undeniably official acts. This was even brought up in oral arguments, where it was asked of Trump's council "if the President ordered Seal Team 6 to assassinate a political rival, would that be considered an official act?" I find it absolutely terrifying that this possibility was brought up, and any mention of the military is conspicuously absent from the majority decision, even in passing (though Sotomayor explicitly brings it up in her dissent).
The most concerning part is how this decision is being made entirely on constitutional grounds. At least in the case of Rowe v Wade being overturned, we have the possible remedy of Congress passing a law enshrining the right to an abortion. But here, there is no legislation Congress could pass to create criminal liability for the President, no executive action. The only option would be a constitutional amendment.