Eg the French Liberté, égalité, fraternité

2.) Morality is not "subjective" to an atheist by default, and I daresay many do not adhere to the idea of moral relativism.

3.) Ethics are derived from biology and culture combined. Biological imperatives… live, reproduce, and protect our friends and families so they can live and reproduce… those give a sound, non-relative basis for a code of decent human ethics. Cultures will have the relative parts, such as whether or not a cow is sacred, for instance… but that will not affect basic ethics relative to one’s right to life, or to be treated equally among peers.

4.) The moral constant is the biological drive to live, and it behooves us to grant others the rights we would like to have in return. We have also, over many generations, come to realize the benefits of altruism, and so we extend the biological "family" circle out to encompass all humanity.

5.) Atheism has no ideology, and I present this only as my own perspective. As it happens, I am an atheist. Secular Humanism, the Brights, the Church of Reality, and more are organizations that offer ideologies for non-theists. There are also older, non-theistic religions, such as Zen Buddhism.

honesty with self can work to bring one to equality among others.
But don’t lose sight of the fact that morality at its base, is simply the knowledge of good and evil. And THAT is something bestowed upon all mankind since sin entered the world.

Atheists are moral because they are human beings. God has not said that only Believers get the knowledge of good and evil.

Atheists are moral because we know the difference between right and wrong and keep to our standards because its the right thing to do.
Christians only do the right thing because they either expect a reward or fear punishment.

You cannot be taken seriously when you say things like "morality being subjective in an atheistic mindset" when what you actually mean to say is "I think morality is subjective for atheists." Atheists do not say that moral views are subjective — that is existential nihilism or, specifically, moral nihilism which is almost universally rejected by thinking people, including atheists, as not a sensible option.

Try reading:
Atheism Explained by David Ramsay Steele

Atheism: A Very Short Introduction by Julian Baggini

I would argue that an atheist who philosophizes about the differences between religious ethics and atheistic ethics would say that atheists are forced to be ethical or not unlike believers who have the additional opinion of just knowing that he ought to look ethical.

Specifically with regard to equality an atheist is left with no other opinion: all human beings are equal or he is a hypocrite. The believer has the option of looking to "holy" texts and tradition to argue that God’s order has another way of looking at things that is "higher" or "better" than equality.

For example:

"Slaves obey your earthly masters in everything;…It is the Lord Christ you are serving." Colossians 3:22-24

"He that gathered much did not have too much, and he that gathered little did not have too little." 2 Corinthians 8:15 (quoting Exodus 16:18). Everything that you have is as God wishes it to be.

To argue that higher modern ideals like equality and justice come from a theistic tradition that isn’t compatible with atheism is to miss, entirely, that those modern ideals became fixed into modern religious tradition by rebellion — rebellion that was by and large denounced at the time by religious leaders as…atheistic (placing man’s law above God’s law and the tradition of the church).

Missing the vile contempt of the religious establishment for such critical thinkers as Thomas Hobbes, Benedict Spinoza, David Hume, Thomas Paine, and John Stuart Mill also means missing that the central pillar of The Enlightenment — reason is the primary source and legitimacy for authority — is a direct and open challenge to the moral authority of religion
.

‘How can an atheist come up with the concept of equality among men’ is also a flawed assumption. You might as well ask ‘How can non-French speakers like ice-cream?’

You are making sweeping, bigoted generalizations (which ironically is demonstrating your own practice of inequality) apparently in a thinly veiled attempt to criticize, & doing so using the deliberate deceit of pretending to present it as a question.

It’s worth pointing out that Warren Buffet & Bill gates, the two individuals to have donated the most to charity, have pledged approximately £35 billion – they are both non-religious & yet are willing to contribute more than any single religious organization (http://news.bbc.co.uk/1/hi/5115920.stm). Numerous charities are specifically or incidentally non-religious e.g. Amnesty International, Red Cross, Gates Foundation, Oxfam, UNICEF, World Health Organization.