Do you believe that homosexuality is fairly categorized into the same group as murderers, violent criminals, and slavers?

For a start, don't truncate what it says. I will reword your question.

"Do you believe that men who practice homosexuality are fairly categorised into the same group as the lawless and disobedient, the ungodly and sinners, the unholy and profane,those who strike their fathers and mothers,murderers, sexually immoral, enslavers, liars, perjurers, and whoever else practices what is contrary to sound doctrine?"

In that case, the answer is yes.

You could reword it to say also "do I believe that liars belong in the same category as murderers". In which case, it depends on the context. Is murder as bad as lying? No. But are murder and lying both sinful? Yes.

To round it off,

James 2:10-11

For whoever keeps the whole law but fails in one point has become guilty of all of it. For he who said, “Do not commit adultery,” also said, “Do not murder.” If you do not commit adultery but do murder, you have become a transgressor of the law.

Romans 6:23

For the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord.

while building a no-true-Scotsman scenario

Quoting that fallacy is fallacy in itself.

James 1:26-27

If anyone thinks he is religious and does not bridle his tongue but deceives his heart, this person’s religion is worthless. Religion that is pure and undefiled before God the Father is this: to visit orphans and widows in their affliction, and to keep oneself unstained from the world.

Probably because scripture also tells christians to beat them to death with rocks.

No it doesn't. That was in the levitical law and was for the jews of that time. The law has been fulfilled through Christ who stopped the stoning of an adulterous woman. (John 8:1-11)

There is no atheist dogma

There is. And that is that "there is no God". Which also naturally follows "There is no final judgement". And if there is no God, one could reason morality doesn't exist. It can and has resulted to cruel acts. Hate and evil knows no creed.

how you reconcile the disparity between the church and the book

I try to live out the change that I want to see, and rebuke those who act unchristlike.

There was a fella a while ago who I presume was just racist. He joined our Christian group and identified as Christian. Then he started spouting absolute vile hatred against muslims and even boasted about harassing them. I took the stand in telling him that even though we see islam itself as a heresy, the way he was acting was not only unconstructive but unchristlike. I guess because I lead, the others joined in an were like "yeah, Flax is right". He eventually got so fed up that we were so "weak" that he renounced Christianity and left us.