There's the usual range of liberal attitudes amongst these men. Some of the more right-liberal ones limit themselves to calls for procedural equality. But others are more radical and want to follow through more consistently with the liberal ideal of making gender not matter.
It's therefore often assumed at MRM sites that masculinity is an oppressive construct; that the aim of the MRM is to liberate men from masculinity; that society should be strictly gender neutral, including in parental roles and in having women drafted into combat roles; and that feminist countries like Sweden are the models for the rest of the world to follow.
The second wing of the MRM are the male separatists (who call themselves "men going their own way" or MGTOW).
These are men who have grown up in an age of female individualism. Their experience is of a society which is geared toward maximising female autonomy, whether it's in terms of education, careers or family.
Movements based on gendered victimhood: they're all crap.