I do not see anything wrong with trying to investigate, because it will either strengthen the faith considerably or it will lead the believer to a faith that has less flaws.
For example here are several articles by mormons about the subject of blood atonement:
fairlds.org/apol/ai048.html
en.fairmormon.org/Blood_atonement
Response
Despite a number of rhetorical statements by LDS leaders in the late 1850s, there is no evidence that anyone was “blood atoned” at the orders of Brigham Young or any other general authority. Contemporary claims for such actions uniformly come from anti-Mormon books and newspapers with lurid titles such as The Destroying Angels of Mormondom and Abominations of Mormonism Exposed.
The First Presidency issued an official declaration on the matter of killing apostates, as a form of blood atonement, in 1889. This declaration reads, in part:
Notwithstanding all the stories told about the killing of apostates, no case of this kind has ever occurred, and of course has never been established against the Church we represent. Hundreds of seceders from the Church have continuously resided and now live in this territory, many of whom have amassed considerable wealth, though bitterly opposed to the Mormon faith and people. Even those who made it their business to fabricate the vilest falsehoods, and to render them plausible by culling isolated passages from old sermons without the explanatory context, and have suffered no opportunity to escape them of vilifying and blackening the characters of the people, have remained among those whom they have thus persistently calumniated until the present day, without receiving the slightest personal injury.
We denounce as entirely untrue the allegation which has been made, that our Church favors or believes in the killing of persons who leave the Church or apostatize from its doctrines. We would view a punishment of this character for such an act with the utmost horror; it is abhorrent to us and is in direct opposition to the fundamental principles of our creed.
Despite the critics’ claims, there is evidence that some crimes were considered worthy of death, even in the apostolic age among Christians:
Whosoever hateth his brother is a murderer: and ye know that no murderer hath eternal life abiding in him…If any man see his brother sin a sin which is not unto death, he shall ask, and he shall give him life for them that sin not unto death. There is a sin unto death: I do not say that he shall pray for it. All unrighteousness is sin: and there is a sin not unto death. We know that whosoever is born of God sinneth not; but he that is begotten of God keepeth himself, and that wicked one toucheth him not" (1 John 3:15; 1 John 5:16-18) (italics added).
As one historian noted,
That the doctrine [of blood atonement] was preached by high officials is a matter of record; the intent of the sermons became a matter of conjecture; and the results therefrom set vivid imaginations working overtime. Blood fairly flowed through the writing of such men as Beadle in Life in Utah or the Mysteries of Mormonism and Polygamy, in Linn’s The Story of Mormonism, and even Stenhouse’s anonymous chapter on Reformation and Blood Atonement in his Rocky Mountain Saints. Numerous killings, including the Mountain Meadows massacre, were credited as the fruits of the doctrine…
Omitted from quotations used by the anti-Mormons were restraining clauses such as follow from Brigham Young:
. . . The time has been in Israel under the law of God that if a man was found guilty of adultery, he must have his blood shed, and that is near at hand. But now I say, in the name of the Lord, that if this people will sin no more, but faithfully live their religion, their sins will be forgiven them without taking life.
The wickedness and ignorance of the nations forbid this principle’s being in full force, but the time will come when the law of God will be in full force.
The doctrine of blood atonement which involved concern for the salvation of those to be subjected to it, could have little meaning in the Mountain Meadows massacre, or any other of the murders laid unproved on the Mormon threshold (emphasis added).[5]
Brigham Young’s preaching style
Furthermore, critics have often misunderstood or misrepresented Brigham Young’s (and others LDS preachers’) preaching style, seeing them in ways differently than the Saints of the day did:
There grew between the Mormon leader and his congregation a bond that permitted…irreverence [toward Brigham personally]. Brigham cast himself as the Saints’ gruff but loving father, alternately scolding and befriending his flock. As lawgiver, he felt he should preach without compromise.
“I will tell you what this people need, with regard to preaching,” he said. “You need, figuratively, to have it rain pitchforks, tines downwards… Instead of the smooth, beautiful, sweet, still, silk-velvet-lipped preaching, you should have sermons like peals of thunder.”
True to his word, Brigham gave saints and sinners pitchforks aplenty. The latter might be especially hard hit if guilty of malicious anti-Mormonism…
But his outbursts were the exception rather than the rule, and even when thundering he often softened his blows with humor…He conjectured that some women’s dresses might conceal a six-horse team, with “a dozen dogs under the wagon.”…Far from rankling under his thrusts, the Mormon membership came to tolerate, expect, and even enjoy the show…
One did not have to go far to find the keys to his speaking popularity. For one thing, his audience sensed that behind his strong words lay a genuine concern". my heart yearns over [the Saints]… with all the emotions of tenderness, so that I could weep like a child," he said, but I am careful to keep my tears to myself." He assured his people that he never intended malice. “There is not a soul I chasten but what I feel as though I could take them and put them in my bosom and carry them with me day by day.”
Brigham believed that his strong words had not separated him from his flock. “Although I may get up here and cuff… [the people] about, chastising them for their forgetfulness, their weakness and follies, yet I have not seen a moment when they did not love me The reason is, because I love them so well.” He had rebuked with caution, he thought, employing a primary rule: “When you have the chastening rod in your hands, ask God to give you wisdom to use it, that you may not use it to the destruction of an individual, but to his salvation.”…
The Saints also understood that there was little bite to his celebrated bark. Young admitted as much. “I have had some people ask me how I manage and control the people,” he once remarked. “I do it by telling them the truth and letting them do just as they have a mind to.”…
