How accessibility access is secure? My android device is rooted and running Android 4.4.2.

Some apps like App Lock, GO Power Master, Kaspersky Internet Security, All-In-One-Toolbox, MoboClean Auto Installer ask for accessibility access for better performance.

All the above apps assure me that they are not gathering any personal information, but while giving access I see a message saying they observe actions and retrieve window content.

What should I do in this case?
Put simply, it isn't secure.  Do not give any apps extra permissions or increased access that you do not trust them with.  Once you give them access to your data, they have the opportunity to abuse it.