This is a summary of the types of political advocacy 501 (c)(3) organizations can legally do. It is taken from this document, put out by the Alliance For Justice at afj.org.
These are federal and IRS rules, states may have different or additional rules.
May not support or oppose specific candidates
May do voter registration, education around elections.
May support ballot measures and advocate for change.
May lobby to propose passage or defeat of specific legislation. Lobbying must not be a “substantial” part of the organization's activities, though “substantial” is not defined legally. No more of than 20% of an organization's budget may be used for lobbying, and only 5% (¼ of the 20%) for grassroots lobbying to voters.
No lobbying can indicate support for particular candidates of parties.
May support or oppose political appointments such as judgeships.
May not work to draft specific candidates or promote third parties.
May not make a pro-candidate message or coordinate with a candidate to promote a message.
May not provide in-kind contributions to candidates.
May do issue advocacy. Should avoid comparing the organization's views with candidates, or mentioning where candidates stand. Put disclaimers on advocacy literature. Don't say things like “vote green” which could be construed as supporting a candidate that says he is green.
May express support of disagreement with an elected official's position or vote, but not advocate for or against that official. It's good if this kind of activity takes place in other than election years as well as in an election year.
May publish voting records.
May invite candidates for an event as long as there is to appearance of support or fundraising. Opposing candidates should have the same opportunities. In educational events, literature and promotion needs to say this is not an endorsement of candidate.
May offer facilities at market rate, even if that's free of charge if that is usual for most community groups.
May sponsor candidate debates or forums if all are invited, including separate events.
May not suggest to employees how to vote.
May ask members to sign or distribute petitions on ballot initiatives.
May not distribute bumper stickers or candidate materials.
May encourage people to vote.
May educate candidates on organization's issues. Should do the same for all candidates.
May ask candidates their views but not for a pledge of support.
IRS form 5768 for major lobbying effort. Doesn't affect non-profit status Found here; good if your lobbying spending approaches 20%
https://www.bolderadvocacy.org/wp-content/uploads/2012/10/Worry_Free_Lobbying_paywall.pdf
Not defined as lobbying;
1. Nonpartisan analysis, study or research that presents all sides of an issue
2. Responses to written requests for assistance from committees or other legislative bodies
3. Challenges to or support for legislative proposals that would change the organization’s rights or its right to exist
4. Examinations and discussions of broad social, economic, and similar problems
Lobbying consists of communications that are intended to influence specific legislation. For electing charities, there are two kinds of lobbying communications; direct and grass roots. They are distinguished mostly by whether the organization is acting on its own behalf or asking members of the public to speak out.