Synonym for "marketing" that doesn't imply selling or profit

Consider Publicity,

Material or information used for advertising or promotional purposes

Usage:

The publicity materials on domestic violence were distributed by members of the NGO.

or Promotion

The publicizing of a product, organization, or venture so as to increase sales or public awareness

Usage:

The promotional events by the non-profit group to increase awareness on domestic violence

[ODO]

You might consider using the word outreach, as it is essentially what marketing is called when you're talking about NGOs who are attempting to raise awareness of their services among affected communities.

Outreach - an ​effort to ​bring ​services or ​information to ​people where they ​live or ​spend ​time:

E.g. The ​centre was ​awarded a ​grant for outreach to the ​homeless.

From Wikipedia:

Outreach is an activity of providing services to any populations who might not otherwise have access to those services. A key component of outreach is that the groups providing it are not stationary, but mobile; in other words they are meeting those in need of outreach services at the locations where those in need are. In addition to delivering services, outreach has an educational role, raising the awareness of existing services.

Outreach is often meant to fill in the gap in the services provided by mainstream (often, governmental) services, and is often carried out by non-profit, non-Governmental organizations.

Raising Awareness

As an expression it is a bit like publicity but without the PR (Public Relations) undertone. Whilst I like the word propaganda, it too has political and other connotations to political and unpleasant