Is it safe to clear data for gallery? I have a Motorola Moto E (Gen 1). I've observed that the gallery app from Motorola takes up 50.13 MB under 'Data'.

My question is: Is it safe to select the 'Clear Data' option? Will I lose the pictures stored if I click on it?
You will not lose any of your photos, if  CLEAR DATA operation is performed, it is completely safe to do so. This just means that your preferences have been reset and the cache has been cleared.1 Cache is generated only for providing fast access to gallery files.

When you restart your gallery after this operation, it'll take some time to load and it will once again show you how to navigate through the Gallery app.  



1: Pressing the Clear Data button automatically clears the cache too. This is can be seen on the screen right then because when you press the Clear Data button and once the data is cleared, you will notice that under the Cache section, Cache shows 0.00KB and the Clear Cache button is disabled too.