No they are not mutually exclusive. Some people could be acting based on what is "coming from the heart" due to egoistic reasons. The ego is just an abstract concept that we pretty much designate for an entity that is inpired by selfish actions, thoughts, and motivations.

So IYHO, when something comes from the heart, does it automatically make that selfishly inspired action righteous; or is something simultaneously labelled righteous and coming from the heart?

Come on, everyone knows that the Ego resides in the Liver.

I think the contextual biases we have towards (ego) and (heart) make them seem mutually exclusive. Words tend to have a central meaning that shifts as their usage and the culture of the people who use them do. Use Ego out of context and the cultural meaning context automatically inserts itself. When someone says ego, the common context has to do with pride and pure self interest. Non-contextualized ego is always suspect. The same process, opposite sense goes for the phrase (comes from the heart). This when said without context is a maxim that is internalized into the cultural lexical ethos to the point of cliche. And without context it will automatically be seen as the exact opposite as ego. As stated above, if abstracted or couched in the proper context they are not necessarily mutually exclusive, but if overheard in a conversation or if they are just thrown out there, they are mutally exclusive by means of the common lexico-cultural understanding of the terms.

Singularity <--------> Universality
Ego (autonomy)<---> heart (relation)

Hi, Holiday! I think that there is no fundamental difference between what they call ego and heart. One may act stupid, out of ignorance when it seems to him that he should try to live according to different patterns that were instilled in him. This ignorance is egoism. But when one knows what is real good for him, he starts to live skillfully. And this knowledge has much to do with virtue, "life coming from hart". I think there's difference only on the level of knowledge.