You are correct that 501(c)(3) charities are prohibited from supporting or opposing candidates for public office (See Ready Reference Page: “IRS Guidance Has Not Changed on Electioneering”) and are limited — though definitely not prohibited — in their lobbying on legislation (See Ready Reference Page: “Lobbying Rules Create Opportunities for Charities”), but the Internal Revenue Service has made clear that they may participate in voter registration drives and Get Out the Vote (GOTV) activities so long as they are conducted in a “neutral, non-partisan manner.” There are no specific limits in the Tax Code or regulations.

Charities are required to operate “exclusively” for charitable purposes. The regulations define “exclusively” as “primarily.” The case law generally provides that “no substantial part” of the activities may be non-charitable.  Even if registration and get out the vote activities are considered non-charitable — and it is not at all clear that encouraging civic participation is not charitable — an organization that carries on a traditional charitable program should not have to worry about adding these activities to the overall program for a couple of weeks every four years. 

I was on a phone call a week ago where two of the participants said their synagogues were registering voters and encouraging voting for the first time that they could remember. There seems to be a view in both parties that this Presidential election could be the most consequential in our lifetime. As part of our cultural ethos, voting is good. Keep up your regular program, but you should be able to do what you can between now and election day to register voters and get out the vote, as you say, non-partisanly.