Religions must not hate each other is very true, the Quran says do not revile other gods or else, through ignorance, they will revile Allah. So when we hate, they may hate us back.
The cow is used in agriculture and is a life giver but to take this to the extreme of not killing some cows for food is wrong. Some do not kill the cow but kill someone who kills a cow, meaning human life less valuable.
Concentrate on god by idol worship is a wrong explanation. When you have an idol, offer it food, venerate it, this is not just a ‘direction’ to look towards to ‘see’ the one, invisible, god, it is idolatry.
As cow and idol veneration is personal choice, we have no right to force them to stop but we have every right to tell them we think they are wrong.
“Adam and Eve had children so their children committed incest with their parents and amongst themselves” is the natural absurd, abominable, appalling conclusion that must be arrived at if we make Adam and Eve to be the first humans. If you think logically, as you claim, then you must reject the absurdities in the religion that are all derived from man made ideas or the wrong understanding of the Quran. It means mankind, not an individual Adam, so the depravity is eliminated by elevating your thoughts to a logical, thinking, higher level.
There should be no struggle between science and a true faith, way of life, not blind beliefs, unless, of course, you reject science for blind beliefs.
By all means, clean up your language, for the Quran says reason with them in the best of ways.
I know of many intelligent people who use their intelligence in one field, eg medical/career, and then do nothing to look at the problems they see in their religious beliefs. Muslims who see wrongs should look at the cause of the wrongs and eliminate these instead of rejecting it all. A Christian was told to reject everything they believed because they could not get a satisfactory answer about an absurdity they had read in the Bible, but could not do this as their ‘community’ was more important to them.
My logical reason for being a Muslim is, that it is most improved my intelligence.