Why do App Locker apps need so many permissions? Am i safe? I've been trying to password protect an app, and it seems that the permissions vary from app to app for App Lockers. 

Why do so many of them require full phone access?

Is there any danger if i use a popular and well known on such as https://market.android.com/details?id=com.morrison.applocklite?
The first part of your question "Why do so many of them require full phone access?". This is for 2 reasons. 


The granularity of the Android permission system groups many system APIs under a small number of permissions. 
App lockers need low level access to disable/enable apps. 


I assume that by "full phone access" you mean something like the "modify global system settings" permission. This permission is probably going to be required by app locker applications to prevent someone from disabling the lock without authorization, but it's hard to say, since I didn't write the app. In the context of this question there are a few other permissions that make sense to me, e.g., "retrieve running applications" and "automatically start at boot". It's likely that most app locker apps will request at least those permissions. 

The rest of the permissions would be unnecessary just for locking an app, but may be used for other reasons. For example, I don't know why the app needs to intercept outgoing calls.

For what it's worth, I ran the apk through http://android-permissions.org, and the tool reported that this app is not over privileged, meaning that inside the app, there is code that makes use of all the permissions requested. This isn't good or bad, it just means that the developer probably isn't requesting unneeded permissions. 

To answer the second part of your question, you are probably ok if you install that app, but we can never be sure. An update might make the app start doing something different that you find unacceptable, or the app may already be transmitting your phone number or IMEI to some remote server. Who knows.