Einstein said
We can not solve our problems with the same level of thinking that created them
So my short and sweet answer is "Pray to God."
Note I am merely using Judeo-Christian language above.
A more eastern answer would be: "When the Truth is known there are no disputes.
To know the Truth we must start by becoming more aware of our own truth."
To me the two answers are the same because Truth and God are the same in most religions. In particular in Hinduism Satyam Shivam Sundaram is a description of God. Literally means: The True, The Good, The Beautiful.
(I am a Hindu by birth but respect all religions)
Note this quite exactly matches the basis set out by Socrates, the starting point of western philosophy: The Good is higher than the True and Beauty is higher than the Good.
[Philosophy mostly deals with only the True because the Good and the Beautiful are beyond words.]
See how close it comes to the starting point of Tao Ching!
In the language of Plato's Republic, the Good has no being but all being arises from it.
The very word 'Platonism' (it should really be Socratism) means:
There is truth; that truth is not in our mind but can be reflected there
It is not in space time but it is manifest in space-time.
You can call it Plato's heaven or Truth or God. Its the same
Coming to your examples:
Abortion
If we take one extreme its murder.
At that extreme one can find hard core fundamentalists who will say ejaculation (masturbation) is murder. Even erection?
At the other extreme the foetus is an unliving entity.
Till what point?
If we take it upto 9th month then 'aborting' a mother in labour would be ok.
Most sane people would find both extremes absurd. Clearly there needs to be some midpoint where the transition happens from male-female fluid mixture to a living being.
If we agree to this much then it becomes a question of agreeing to a point where discarding a hair or a nail transforms into a moral question.
Why can people not have such a discussion? Because people in a confrontation take extreme positions.
To not take confrontative positions we must follow Jesus Christ teaching: "Do not judge." Because if we stop judging we may listen to the other party.
BTW a particular Indian nonsense regarding abortion.
In USA feminists are pro-abortion because they are pro "choice".
In India feminists are anti-abortion because selective female foeticide is a particular Indian problem. So that ultra-sound clinics have government notices saying sex determination is a crime punishable by 50,000 rupees and jail for 5 years etc. Such notice is considered PRO feminist.
So a consistent feminist sitting in a Mumbai-New York flight needs to flip her stand half way!!!!
So much is a bad joke. But it has a serious part.
Suppose India and USA were to merge into a larger country.
And suppose we were framing the Roe-Wade controversy for this super-country.
Which way should it go? Which choice is the feminist choice?
LGBT theory
Some very great people have suffered and died just for being LGBT eg Alan Turing, Oscar Wilde. In modern times Chelsea Manning is a great person and a hero.
These examples tell the horrors of the old default anti-LGBT model.
So should rapists be allowed to be in women's prisons by just claiming to be trans?
Should a man can enter a women's wrestling competition and break the opponent's skull just by claiming he is a she?
So hard and fast rules are not the way. Detailed careful discussions are needed.
Why they dont happen?
Because we judge and not listen.
Why this?
I believe this is because of the peculiar nature of Christianity.
[Just to make clear: I have the highest regard for Jesus Christ as a rishi, as a guru as a healer. In India such a man would be called "mahatma" -- great soul]
The problem is that 300 years after Jesus in the Nicene council the gnostics were murdered and wiped out. What this meant is that the wisdom side of Christianity disappeared and only the faith devotion, side remained.
This is very very unfortunate and the source of much of the western world's problems.
In the Bhagavad Gita Sri Krishna teaches Arjuna the way of jnana and bhakti, in modern language philosophy and religion. Arjuna tries very hard (18 chapters!!) to make Krishna commit to one or other. But Krishna cannot be pinned down!!
Likewise Buddhism is a system of psychology. To therefore use that to say Buddhism is not a religion would be absurd.
So we can say that the wisdom-devotion pair can be found in all world religions. Its just that in Christianity it has to stay more hidden because of this absurdity that knowledge is considered antithesis to faith.
So in short I would like to say:
The mystic Hermes Trismagistus said: "As above so below"
The division of ourselves and the division of the world is two sides of the same reality.
The fracture of faith and wisdom was created externally by the Nicene council.
After that it has become a feature of the Christian heart.
From there it has become a feature of the Christian world. Now even after the effective erasing of Christianity from our modern world the fracture remains.
Many people will retort: We have no interest, connection with religion.
Dont talk religion to us.
So I say, Just replace: "wisdom-faith" by "facts-values".
There you see the basis for the modern fractured world.
[Apologies if this looks like "conversion" attempt. There is no such concept in eastern religions. My suggestion (wish) is that for you to get beyond polarization you find in whatever religion, philosophy, teaching you like the faith part and wisdom part TOGETHER.
All Abraham's descendants can do that but it may be a bit hidden.
Its just a bit easier for us eastern people
]
Added later
quarague asked this. Some 6 others upticked the comment. So I assume its worth a clarification
Relation between compromise and religious orientation
This is a correct question.
The meeting ground is humility. One does not go for a compromise-finding line without a modicum of humility. The only guaranteed way of fostering humility is a religious upbringing. People may argue that humility can and does arise in secular day to day life also. eg if one is a doctor, scientist, engineer... and encounters someone enormously better. But a careful self-examination at that point would reveal that there is always some admixture of envy, jealousy, greed etc there. Towards a transcendent entity, that is impossible:
O God you are so great I cannot make the universe as you can. But I built my own house. Do pat my back and tell me its half as good as you!
Can such a feeling ever arise? I dont think so. So the habit of humility inculcated in religious oriented childhood can then get translated into the mundane world.
Added later
Specifically in answer to people who think religion is the problem not the solution:
This guy (don't know his name) says what I am saying better than I did.
[Note I am underscoring the first one minute or so. The remaining part is more political but also more divisive. Choose from it as you will. For this answer I am referring to the first part]