We have to answer this question differently for an atheist, versus an atheist activist.
Compared to many other countries with majority muslim population, being an atheist in Turkey is not as bad or as difficult as one might think. There are no laws that require the prosecution and punishment of atheists solely because of being atheist, and someone’s life is not in danger simply because of being an atheist, usually. Danger of physical harm (getting beaten by a mob, etc) is also not an issue usually, for most people, in most settings (although there may be exceptions).
This would be the situation most atheists would find themselves in, but only when this is only known by a limited number of people, such as their social circles, or their community. They may feel discrimination, bias and other difficulties in the workplace and within their extended community, but usually not to a degree that would endanger their lives or put them in risk of physical harm.
Some may be lucky enough to not even experience any of that, if their social circle is more accepting to their identity. Those people may be able to live openly atheist lives in Turkey without any significant negative consequences or difficulties.
But those would be in minority. Most atheists would face more issues, if they are openly atheist. A lot of atheists in Turkey would be forced to live their lives as closet atheists, or suffer difficulties and discrimination from the others around them.
For public figures, the situation would be a little more different. If someone is a public figure, and openly atheist, they may still be okay, as long as they don’t make their atheism a central aspect of their image and their outlook, and as long as they are not atheist activists.
But if someone is an atheist activist, their lives would be a lot more difficult, especially if they are well known, or if they are public figures.