Did women's social and political standing change at all during the late nineteenth century? If so, in what ways? Were these changes for the better?

If only everything in the world had a linear, direct causal relationship.
Perhaps, towards the end of the 19th century there were some relative improvements to, say, the social and political standings of females compared to their predecessors who lived hundreds of years before them. Change is always happening, yes.
But, I would argue the rate at which it occurs is the main question. I am afraid that many female academics, artists, and politicians of the late nineteenth century did not live to see their work and contributions appreciated by the masses. Even now, females are overshadowed.
As an extension, you will see that it is not until the early twentieth century, do we see a large scale, massive opening of post secondary education to females.
As for the politics and social aspects, I believe that many individuals in the current year(2018) are still stuck peddling outdated ideology, by virtue of sexist remarks, pseudoscience, and biological essentialism.

Women rose in social and political stature in the late nineteenth century, inspired by women's rights activist Susan B. Anthony. During the Civil War she collected thousands of signatures to abolish slavery. In 1868 she and Elizabeth Stanton co-founded a women's rights newspaper called The Revolution, then helped launch the National Woman Suffrage Association the following year.
In 1872 Victoria Woodhull, a leading figure of the women's suffrage movement, became the first female to run for U.S. President, even though it was still illegal for women to vote. In 1878 Anthony and Stanton presented their idea allowing women to vote to U.S. Senator Aaron Sargent, who introduced the legislation to Congress. It became the Nineteenth Amendment and was ratified in 1920.

The role of women in society and politics changed greatly during the late 19th century. In America, these major changes occurred during the Industrial Revolution. For the first time, women were active participants in the economy. Single women in particular flocked to urban areas in search of work. Young women would leave the family home in search of financial independence. While many still expected women to be mothers, wives, and homemakers, it was not unusual for a woman to contribute to the family income or to pursue a career of her own.
As women established themselves in the workforce, they became more involved in the political happenings of 20th-century America. Many led or participated in labor unions and strove to improve working conditions, limit working hours, and establish child labor laws. Inspired by their influence in the economy, women also became involved in political movements, such as the abolition of slavery and the rising feminist movement. Some of the most influential women of the 19th century were activists and business owners.