"advocate equality" is correct and can be used in written English.
You can use it to refer to someone who promotes or speaks in favor of equal rights and opportunities for all. For example: "During his speech, the mayor advocated equality for all members of the community regardless of gender, race, or religion."
The nonviolent campaigns he waged to bring about equality between Indians and whites over the next 20 years would lead him — slowly and unsteadily, but inexorably — to advocate equality between Indian and Indian, first across caste and religious lines and then between rich and poor.
Generally, our mission is to advocate equality within sex workers.
The great thing about feminism is that the only rule is that you advocate equality.
Nobody seriously advocates equality of outcome.
She became famous for advocating equality and died in 1883.
Polly Toynbee in a brief email seemed to be advocating equality of criticism.
We insist on putting people first, carrying forward a humanitarian spirit and advocating equality and opposing discrimination".
We meet at her office in central London where Morrissey – a bright-eyed Audrey Hepburn of the FTSE100 – has been advocating equality in business for years.
The official party platform emphasizes free-market policies, and it clearly advocates equality regardless of faith or gender, although women and young people had traditionally played little role in the Party leadership.
It has been argued that every conception of justice relies on a specific interpretation of the concept of equality: even libertarianism can be considered as a theory advocating equality of negative rights, and utilitarianism as a theory advocating equality of marginal utility (Sen 1995).
"This is the first domino," said Patrick Burke, a scout with hockey's Philadelphia Flyers and the founder of You Can Play, a group advocating equality for athletes regardless of sexual orientation.
