In the mid-1940s, when the founding members of the vegan movement organized themselves into The Vegan Society they set out a clear purpose for the movement that "seeks to abolish [humans'] dependence on [other] animals, with it inevitable cruelty and slaughter, and to create instead a more reasonable and humane order of society. Whilst honouring the efforts of all who are striving to achieve the emancipation of [humans] and of [other] animals."
I think the intentions of the vegan movement expressed above can be summed up as 1) radical social change that centers the marginalized oppression of other animals, and 2) solidarity with all other anti-oppression movements. The later of these intentions is echoed in the Combahee River Collective's "A Black Feminist Statement":
In the practice of our politics we do not believe that the ends always justify the means. Many reactionary and destructive acts have been done in the name of achieving "correct" political goals. As feminists we do not want to mess over people in the name of politics. We believe in collective process.
In 1964, 20 years after the founding of the vegan movement, Eva Batt succinctly wrote, in her article "Why Veganism?," that "veganism is one thing and one thing only – a way of living which avoids exploitation whether it is our fellow [humans], the [nonhuman] animal population, or the soil upon which we all rely for our existence."
Honoring other social justice struggles is unconditional. If others are being oppressed we should support their efforts towards liberation and avoid perpetuate their oppression. If we, say, promote a multinational corporation exploiting tomato pickers because it presumably makes "veganism" more convenient, then we are not honoring their (in this case the Coalition for Immokalee Workers) struggle to archive emancipation, and we are, in fact, exploiting those workers for the privilege of some supposed convenience. It shouldn't matter if those in other movements aren't vegan, nor should it matter if they are even antagonistic towards veganism. Their oppression matters regardless.