No one else's truth can be Absolute Truth for me. Others can share with me their thoughts, others can give me their ideas, but I have to make up my own mind about what is true for me.
"Absolute truth" is defined as inflexible reality: fixed, invariable, unalterable facts. For example, it is a fixed, invariable, unalterable fact that there are absolutely no square circles and there are absolutely no round squares. That is because squares and circles are defined by truly objective rules that are not subject to debate.
Absolute Truth in a religious context is generally not objective. Most religions define some things as "unknowable" or that we must accept certain things that we cannot verify with rational thought (i.e. we have to accept it on faith). As Ayn Rand put it in Atlas Shrugged:
They keep telling you what it is not, but never tell you what it is. All their identifications consist of negating: God is that which no human mind can know, they say—and proceed to demand that you consider it knowledge—God is non-man, heaven is non-earth, soul is non-body, virtue is non-profit, A is non-A, perception is non-sensory, knowledge is non-reason. Their definitions are not acts of defining, but of wiping out.
Absolute Truths not based on objective principles are not Absolute Truth, regardless of who—or what—they come from.