So my point remains.
Second, Pope Francis can be accused of ambiguity in his published letter, but not an outright denial of dogma.(We might express frustration that he often fails to put his statements into the kind of clear declarative sentences needed for either doctrine or heresy; but grammatical incoherence is a separate issue.) Simply copying what you posted, here's what he said:
"(1)The mercy of God has no limits if one turns to him with a sincere and contrite heart; (2) the question for one who doesn't believe in God lies in obeying one's conscience. (3) Sin, also for those who don't have faith, exists when one goes against one's conscience."
(1) Is true.
(2) Is a question. Indicated by the words, "The question ... lies in ..."
(3) Is true.
Does Pope Francis actually delineate the answer to this question at #2? He does not --- owing to the ambiguity of his statement. He says "the question.... lies in obeying one's conscience," but it does not state that the "answer" lies in obeying one's conscience.
At this point, I can imagine irate people waving their hands in the air and saying, "But he must have meant 'the answer is', who would be so obtuse not to realize that?"
Still, 'question' and 'answer' are not synonyms. This remark of Pope Francis' does not --- as far as I can see --- give us any further definition; neither does he try to illustrate what he means and what he does not mean, using examples or casuistry.
Saying that the 'answer' lies in obeying one's conscience, would be true --- even in the case of a false conscience --- if the defects in the conscience were not the fault of the person, i.e. not the product of malice, pride, sloth, lack of moral diligence, etc. Say your parents taught you that Christianity is both bogus and wicked. Say you are not old enough or mature/experienced enough to seriously suspect that your parents might have been wrong.
You are still objecively in the wrong. This error of yours is objectively gravely harmful to you and to others (as you perhaps influence them in an anti-Christian direction). But you have not committed a (subjectively) damnable sin by following your (erroneous) conscience, because you lacked the requisite knowledge.
This falls under the category of "invincible ignorance." All Catholic moral teaching recognizes that only voluntary and free acts are imputable.
But that's beside the point. The point is that Pope Francis doesn't get into fine definition or legitimate casuistry, he just makes an unsatisfactorily ambiguous statement. It fails as clear teaching, but it's not heresy, which is something both unambiguous and deliberate.
To say that this is heresy is incorrect. To say "The Pope has no business being so ambiguous; he sows sows dangerous confusion when he says this kind of thing" --- well, as far as I can see, that would be true.
But Bergoglio refused to tell a Lutheran woman, who was married to a Catholic, that she was forbidden to receive Holy Communion in the Catholic Church.
Instead, he told her to follow her "conscience", knowing full well the consequences of a false conscience: sacrilege.
(1) Is true
(2) and (3) Together imply a relativism in conflict with objective truth, i.e. that obeying "one's conscience" (no matter how ill-formed) is sufficient to avoid "sin".
But that's beside the point. The point is that Pope Francis doesn't get into fine definition or legitimate casuistry
The statement you have parsed (while ignoring its larger context, i.e. that it is a public statement directed to a militant public atheist and his fellow travelers) is a clear example of casuistry by omission. It implies to the reader that personal conscience (even a conscience that leads one to reject God) is "sufficient to avoid sin". But is not the decision to reject God a sin against Charity?
"And we have known, and have believed the charity, which God hath to us. God is charity: and he that abideth in charity, abideth in God, and God in him." 1 John 4:16
"Their inculpable ignorance will not save them; but if they fear God and live up to their conscience, God, in His infinite mercy, will furnish them with the necessary means of salvation, even so as to send, if needed, an angel to instruct them in the Catholic Faith, rather than let them perish through inculpable ignorance." (St. Thomas Aquinas)
One cannot "fear God" while simultaneously rejecting Him.
It fails as clear teaching, but it's not heresy, which is something both unambiguous and deliberate.
Again, the statement you have parsed misleads by omission. When considered alongside other public statements by our Pope (including some which contain strange Scriptural additions and interpretations that apparently contradict the teachings of previous Popes and Tradition) a troubling pattern has emerged, and that being the case, it seems a tad fruitless at this point to be parsing and arguing over individual bits and pieces of his questionable statements.