This is a great question, Martin Luther King speaks about the hippie movement directly in the spring of 1968 in one of his last essays.
Dr. King wrote an essay on the state of the civil rights movement. In it he speaks about the Youth and their Social Action breaking them up in to three main groups, young people struggling to adapt to the prevailing values and rules of society, The radicals and lastly hippies. He didn't speak that glowingly about the Hippie movement. Below is a quote from the essay.
"They are struggling to disengage from society and to give expression to their rejection of it. They disavow responsibility to organize society. Unlike the radicals, they are not seeking change but flight. When occasionally they merge with a peace demonstration, it is not to better the political world but to give expression to their own world. The hard-core hippie is a remarkable contradiction. He uses drugs to turn inward, away from reality, to find peace and security. Yet he advocates love as the highest human value; love, which can exist only in communication between people, not in the isolation of the individual."
"The hippies cannot survive as a mass group because there is no solution in escape. Most of them will regroup, either joining the radicals or drifting back into the mainstream. Some of them may persist by solidifying into a secular religious sect. Their movement already has many such characteristics. We might see some of them establish utopian colonies like the seventeenth and eighteenth-century communities established by sects that profoundly opposed the existing order and its values. Those communities did not survive, but they were important because their dream of social justice and human value continues as the dream of mankind. In this context one dream of the hippie group is very significant, and that is its dream of peace. Most of the hippies are pacifists, and a few have thought their way through to a persuasive and psychologically sophisticated peace strategy. Society at large may now be more ready to learn from that dream than it was a century or two ago; it may listen to the argument for peace, not as a dream but as a practical possibility, something to choose and use."
He basically feels that they cant be trusted and because they have no goal, they would drift back in to one of the other major groups.
Martin Luther King's thoughts on Feminism are not nearly as direct, we kind of have to infer from his actions his ideas on feminism.
He founded the Southern Christian Leadership Conference with the Rev. Ralph Abernathy and from the beginning it was a very male dominated organization with Ella Baker being the only woman in the central leadership. She would later complain in her biography about the preachers.
“not ready to welcome her into the organization on an equal footing” because to do so “would be too far afield from the gender relations they were used to in the church.”
These complains would led Ella to leave the SCLC and found the Student Nonviolent Coordinating Committee (SNCC)
King did support contraception and the work of Planned Parenthood, after his assassination in April of 1968. Coretta Scott King would take a larger role in the civil rights movement and expand it to include Woman's Rights.
More Reading:
A New Sense of Direction by Martin Luther King, Jr.
https://media-1.carnegiecouncil.org/import/publications/4960_v15_i004_a002.pdf