Someone said that if you vote from abroad you will be reported to your state tax office and get a tax bill.
Voting in federal elections cannot be a basis for a state to assert tax liability on its overseas voters.
This is exactly the type of scare-mongering myth that keeps Americans abroad away from the ballot box. Don't let it keep you from making your voice heard.
The key in this equation is whether you vote for local and state offices, or just federal offices (President, Vice President, US House of Representatives and US Senate).
If you consider yourself as living temporarily abroad with an expectation that you will return, and you are continuing to pay state taxes while abroad, then you will likely receive and choose to vote a full ballot, including local and state offices.
But if you are living abroad indefinitely with no fixed plan to return, it is wise to refrain from voting for state and local races, and vote only for federal offices. You are never obligated to vote the full ballot, even if you receive it. You can vote only for federal offices and return your ballot with confidence that it will be counted, regardless.
It is illegal for a state to assert the use of its voting infrastructure in federal elections as a basis for asserting tax liability on the part of its foreign resident ex-residents. Expats can vote in federal elections without fear that doing so will affect their status vis-a-vis the state tax authorities.