Since it promotes the prioritization of career over family, is feminism a capitalist or Marxist movement?

The way things work in the US traditionally, both career and family support capitalism. Capitalism causes a toxic hierarchy where people obsessed with power and feeling important are the ones most likely to make it to the top and rule over everyone else. 

And our culture pushes the idea that men are the natural leaders of the world, who should be in powerful positions, making it easier for them to move up in the workplace. 

Then look at all the churches today STILL teaching that women need to submit to their husband's authority. Both family and the work place could be more marxist, but current cultural beliefs are creating capitalistic hierarchy in both areas, and causes people to act abusively.

It grows from a desire to be treated right.

Feminism promotes allowing women to have choices in their lives and not just pushing them towards marriage and motherhood like social conservatives want for them.

The OG feminists were fighting to be allowed to participate in Capitalism but of late sadly all their efforts are being undermined. 

Some feminists support capitalism, others support Socialism.  Some want equality under capitalism, others want a society where everyone is free and equal. 

Feminism does not promote career over family, it promotes choice, where one does not have to give up their career if they do not choose to.  It is neither Marxist nor capitalist, but liberal, since liberal is about freedom.

If it had actually been career over family, as you thought, then I would say capitalism since Marxism is about what is good for the country, not is what is good for the individual. 

The pattern I see is that the Left tries to hijack the movement, so that the only noticeable part of the movement is far Left. For instance, trans people and sports, gay weddings and cakes, any sort of weather and Climate Change, etc. The Democrats like to hijack these things so that the public thinks the people in those groups are ALL like that.  The Climate Change movement was started by Al Gore, and it rapidly changed from Global Cooling to Global Warming. Then to Climate Change. The notion of science falls to the politicization and news media hijacking of the idea, somewhere in there is still a grain of truth. Feminism means different things to different people. That was hijacked by the Democrats years ago. Even the NOW organization was hijacked by the Democrats. 

Marxism is clearly not about family. So you can scratch that one off the list.