When a Christian says there is "objective morals", is it safe to assume s/he means "my morals which I think?

Yes, more or less. Christians believe certain moral laws are 'absolute'. But what makes them absolute is not that most people agree with them, it's that they are the Word of God.

Christians are taught that their own morals are absolute, which leads to the argument that a person can't be a moral person or live a virtuous, justified life without subscribing to their particular beliefs. Usually they only hint at this but sometimes they'll come right out and say that their religion is the exclusive path to genuine morality.

The fact is, there is no real evidence that morality is absolute or objective. Or simple. The closer you look at morality the more subjective and conventional and complex it seems.

Everyone thinks that other people should essentially share the same morals as they do.

I'm an atheist and I think that too: I think everyone should essentially have the same morals as I do, which are basically respect for life, liberty and the happiness of others. If you didn't think other people should have at least somewhat the same morals as you do, that would mean you'd have no problem with people thinking it's okay to murder.

Edit: I don't see how perfection is in any way relevant or changes the issue. The perfect is the enemy of the good. Everyone still thinks everyone else should essentially agree with them on moral issues.

Edit 2: Well you have a genuinely good point in that clear-cut lines of good/bad are of course flawed. Morality isn't a binary thing, it's a vast spectrum from good to bad.

This is the first time I've ever encountered that term. If someone told me that I would ask them what it is they meant by it. As a Christian, I do my best to live by the standards outlined in God's word the Bible. I know these are best for me personally. I also believe that if everyone adopted and lived by them the world would be a better place.

No. Christians mean that there is a moral law established by God for the "best"

functioning of the world He also created.

There is an absolute "plumb line", and the further we deviate from that absolute

plumb line, the more crooked --- and prone to self-destruction -- the whole house becomes.

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"And he brought me thither, and, behold, there was a man, whose appearance

was like the appearance of brass, with a line of flax in his hand,

and a measuring reed; and he stood in the gate."

Ezekiel 40:3

"Thus He showed me: and, behold, the Lord stood upon a wall made by a plumbline, with a plumbline in His hand. And The Lord said unto me, Amos, what seest thou?"

"And I said, A plumbline."

Amos 7: 7, 8(a)

If there is objective morality, why would God says homosexuals must be put to death in OT and that they must be treated with compassion in NT?

There are several examples in the Bible, where God himself has relative morals

The morality God changes throughout the Bible

That would be subjective then.

And actually that wouldn't even make sense. A moral is an absolute, so it's not subjective.

No

God's Morals , which HE thinks everyone should have

Lets face it, if we did things God's way, there would be no STD's no single mommies, no abortion, no drugs, no alcoholism

sounds pretty good to me

just about everything that's wrong with this world can be traced back to some rejecting the morals of God

There are, indeed, objective morals, as enshrined in the Ten Commandments. They have never, ever changed. Jesus used them to sum up the whole law of God as, to love God with your entire being, and to love your neighbour as yourself.

Perfect morality never needs to compromise; it never bows to wandering stars of fashion or political correctness. The Ten Commandments appeared around 1446 B.C. and they have never been changed. Jesus stood by them and lived them out and tells Christians to do the same. So I don't ever speak of "my morals", and I don't know any Christians who do.

Look up Proverbs 12:10.

one cannot say one is objective with morality if they mean what morality means to them

it is written in the bible, to seek first the kingdom of God and His righteousness. not ours, not what atheists wrestle the scriptures to mean, nor what government says.