Safe to have flight stops at Istanbul?

Of course your question is very subjective and there won't be a correct answer, but I want to give you some details on the safety layout of the airport in Istanbul.

I went through the airport this January (before the bomb attack in central Istanbul) and as opposed to other airports that I have been too, there was an additional security check right at the entrance of the airport where the taxis stop. This is quite a thorough check with scanners and metal detectors and it would be quite difficult to get anything like a gun or a bomb through that. As a matter of fact, this was the only time in my week in Istanbul where I thought a safety check was actually serious (as compared to those at the attractions inside the city). I believe those checks where also the reason why the recent attacks happened at the taxi stands (afaik) and not inside the airport like those in Brussels.

Considering this, and the fact that you are just transiting and probably not leaving the airside area of the airport, this puts at least two check points between you and any potential attacker from the outside and should make it relatively safe inside the airport.

Of course safety is always subjective, and you might argue my argument doesn't hold up for any threat coming by plane or already being inside the airport.