Word for "outcastness"

See if ostracism suffices. Check out this definition at Oxford dictionary:

Exclusion from a society or group.

You might consider the word alienation. As dictionary.com defines it:

alienation (noun):

1. the act of alienating, or of causing someone to become indifferent or hostile: The advocacy group fights against prejudice and social alienation of immigrants.

2. the state of being alienated, withdrawn, or isolated from the objective world, as through indifference or disaffection: the group's alienation from mainstream society.

Although I like vocabulary.com's highly-evocative definition best:

alienation

An easy way to experience alienation from your nice-smelling friends is to go a month without bathing.
Alienation is a state of being cut off or separate from a person or group of people.

The noun alienation describes the feeling that you're not part of a group. Your political views might cause you to feel a sense of alienation from the rest of your family, or your vegetarianism could result in alienation from your meat-eating friends. The Latin word for alien is alienus, "belonging to another." That idea of not belonging, or not fitting in, gave rise to the Latin verb alienare, "to estrange," which alienation comes from.

Marginalization may be a useful word for you to use.

"Instead of physical obstacles, both are faced with societal resistance and marginalization."

In your example sentence, it sounds like the problem is a little less absolute than "ostracism" would imply. Ostracism is when they are excluded entirely, little to no interaction, full stop. Marginalization is a little bit less extreme, they are pushed to the edges, not taken seriously or not well accepted. To me this fits better with "social resistance", which seems to imply something more like dislike and disagreement rather than opposition or outright refusal.

Social exclusion, or social marginalization, is the social disadvantage and relegation to the fringe of society. - wikipedia

or

Marginalization - 1) to place in a position of marginal importance, influence, or power; 2)to relegate to the fringes, out of the mainstream; make seem unimportant - Dictionary.com

Ostracism, as noted by vickyace, seems the apt word, but there's also shunning, a practice used by some religious communities, e.g., the Amish, to brand those who have violated social norms as outcasts with whom community members should no longer have any relations.

Another word that has religious overtones, but is occasionally used in other contexts is excommunicated.

E.g., dictionary.com lists one of the definitions for excommunicate to be "to exclude or expel from membership or participation in any group, association, etc." and as a usage example lists "an advertiser excommunicated from a newspaper."