The radio buttons in a person's profile page on ancestry appear to be an opportunity to override ancestry's general rule of privatizing all persons under 100 years old without a death date. I believe this is a one-way override. That is, I think you can override a person without a death date to be dead, but you can't override a person with a death date to be alive via the radio buttons. I may be wrong on that score, I haven't tested it.
Or, if you have not entered birth dates for people, you can simply use the radio buttons to designate living or dead.
FTM, on the other hand, has no such override.
FTM has a temporary and permanent privatize function. The problem with both is that it uses 120 years instead of ancestry's use of 100 years, or the 70-80 years that a lot of people have used in the past. It doesn't allow the user to designate the opportunity to change the number of years.
For example, if you privatize today in FTM, it will privatize everyone born after 02/10/1893 without a death date or place entry (Note you can enter some acceptable text strings into the date field, like DEATH, INFANT, etc. See Help file Keywords).
The temporary place in FTM to privatize a file for viewing or leaving names out of reports is at File > Privatize. This won't effect your file, its just a viewing and reporting switch.
The permanent place to privatize a file is to File > Export and choose the option to privatize on exporting.
It should be noted that the filter that FTM uses doesn't always work. I am still finding people born in the 1700s that it privatizes. Some people have even reported on this board people born after 1893 as public info, although I haven't seen that myself.
You could also privatize a file by using something different than 120 years after birth as a filter, if you have entered birth dates for everyone in your file. You would filter for everyone in your file born before 02/10/1903 and export that dataset. You might use this, for example, to send a file of ancestors to a fifth cousin, who you don't really want to give info on living people to.
If you want to see how FTM works, go to your index and change the sort to be by birthdate. Also change the display to show the actual birthdate (ie don't use life-span).
This will show everyone in your file listed by birthdate, oldest on top.
Now, File > privatize.
The names of all people continue in the index, but info on privatized people, including their birthdate, will have disappeared. Thus you can see the effect of what the privatize function does.