Vote absentee and if it's really important send it in certified return receipt requested. I did just that in the last presidential election.

It's no different when applying for a job and getting your credit run or a drug test. People find out things about you that are personal and confidential. I remember years ago, even before all this technology, when I learned of a woman in my company having an abortion. This information "leaked" from the Human Resources office. At the time they were handling insurance claims and saw the information in her medical record. I really don't know if that was true, but nothing is really completely private. I can't believe that for whom we vote is always kept confidential, but how would we know?

To answer your question, "Your vote, is it a secret?" -

Yes, your vote is a secret. However, your political affiliation, whether you are republican, democrat, or other, is not. The polling places are designed in such a way as to be systematic and easy for voters. There is a polling booth assigned for democrats, another one for republicans, and other booths for other political parties. The color-code on your sample ballot should be the color of your party; and if you go to the polls, the pollworker will first look for your name on the registered voters list, than check how your are registered (whether republican, democrat, libertarian, independent, etc), and then, direct you to the proper polling booth. The booths are also color-coded to match the code of your sample ballot and your party affiliation.

For example, a republican booth is color-coded red, and your republican sample ballot is color-coded red. That makes it easier for pollworkers to direct the voter to the right booth.

Last elections, I volunteered as an election inspector in my neighborhood polling place. There was one voter, an independent, who insisted he wanted to vote republican and wanted to go to the republican booth. He was getting quite agitated, thinking we were trying to dictate how he should vote. I quietly explained to him the process and pointed to the color-code of his sample ballot which he had in his hand. I assured him he can vote any way he wanted even if he goes to the proper booth.