[millefleur]

One way some telepathy phenomena can be explained is by what the Bible calls "familiar spirits". In other words they are spirits that are familiar with a certain human and can communicate by interjecting words (thoughts) into the mind.
The Bible of course condemns encouraging this sort of interaction.
In the Old Testament there was an account of God causing a donkey to speak with an intelligible voice.

In this case a spirit could be at work with the parrot and the owner but not of God, simply to cause confusion and deception which God allows.

[sweetliberty]

And it could be simply that many animals have highly tuned senses that we do not relate to and might mistakenly refer to as "telepathic." They do sometimes seem that way. I think the word itself may be being used too loosely. For example, a lot of animals react to changes in weather or an impending storm or earthquake well before their human counterparts. Some people would consider that ESP of a sort. Just because we may not understand something doesn't mean that it doesn't exist or that God has nothing to do with it.

[StolarStorm]

My wife and I can read each other's thoughts often... and I'm not talking about thoughts that would be obvious based on what was going on at the time. Out of the blew, She or I will answer a question that the other was thinking. We also tend to call each other at the same time (and these times are not consistent during the day), causing busy signals on both ends. Somehow, I don't think some kind of evil spirit is causing this...

[mercy]

Oh please. Now tell me the 'gifts of the Spirit' are sorcery.

[weegee]

Here is an account of something I caught on the news over 20 years ago:

Famous Guests at the Aquarium: Hoover (the talking seal)

The audio sample they offer is very poor compared to what I heard on the news but it does sound remarkably like Ted Kennedy (and yes this seal has a Boston accent).