There can be a difference of meaning.
What does it mean for a survivor to forgive the gunman?
That can mean, What are the emotional and psychological implications, for the survivor, to forgive the gunman? That is, "for a survivor" focuses attention upon the survivor as the sentient being.
What does it mean that a survivor forgive(s) the gunman?
Although this second formulation means much the same as the first, the emphasis is on the verb forgive, and even though there must be one to do the forgiving, the question is posed more abstractly.
An even greater distinction can be made with the question about Christians, where "for Christians" would focus on the implications, for those Christians, of getting involved in politics, and "that Christians" could even be understood to be placing the focus on the electorate at large, that is, what does it mean for the country when Christians get involved in politics? Or it could be a question about that nature of the involvement, from a political point-of-view.
As for grammatical analysis, the questions could be understood in two ways.
You could be asking about the language itself:
What does it mean for "a survivor to forgive the gunman"?
Or you could be asking about the real-world referents of the words:
What does it mean, for the survivor, to forgive a gunman?
The preposition "for" operates differently, depending on the meaning. In the question about the language per se, the object of the preposition for is the entire phrase inside quotation marks. In the question about the real-word referents of the words, the object of the preposition *for" is "the survivor".
The verb "mean" also has different meanings as well. In the question about the language per se, the question "What does it mean" could be paraphrased "What do the words signify?" In the question about the real-world referents, the question "What does it mean" could be paraphrased as "What are the effects upon, or the emotional implications for, the survivor?"
