VISTA, since they're participants in a federal program, fall under the auspices of the Hatch Act.
The VISTA Handbook addresses a lot of this specifically. Taken from the handbook (and reformatted for web with links added to appropriate sections of U.S.C and CFR. along with personal footnotes):
PROHIBITIONS ON POLITICAL AND LOBBYING ACTIVITIES
No Corporation appropriated funds shall be used to finance, directly or indirectly, any activity designed to influence the outcome of any election to federal, state, or local office or any voter registration activity, or pay the salary of a Corporation employee who engages in any such activity.
In addition, AmeriCorps*VISTA programs are prohibited from using funds or personnel in a matter supporting or resulting in the identification of such programs with partisan or nonpartisan election activities, in voter registration activities, and in providing transportation to the polls. Additionally, no AmeriCorps*VISTA member or employee of a Sponsoring Organization may take any action with respect to a partisan or nonpartisan political activity that would result in the identification or apparent identification of the AmeriCorps*VISTA program with such activity, see 42 U.S.C. § 5043 for additional restrictions and prohibitions.
AmeriCorps*VISTA programs also are prohibited from any activity intended to influence the passage or defeat of legislation or proposals by initiative petition, see 42 U.S.C. § 5043 (c) for additional restrictions and prohibitions.
You may participate in political activities allowed under the Hatch Act. The Domestic Volunteer Service Act at 42 U.S.C. § 5055 applies the restrictions of the Hatch Act, Title V, United States Code, Chapter 73, to AmeriCorps*VISTA members. The Hatch Act applies to you at all times during your service, including off duty hours . Permissible activities under the Hatch Act apply to AmeriCorps*VISTA members unless prohibited by other statutory authority when the members are on authorized leave or are not perceived to be performing as an AmeriCorps*VISTA member (e.g., while not engaged in performing service, or on service time), 42 U.S.C. § 5055.
You have the right to register and vote as you choose, express opinions about candidates and issues in a non-public context, contribute money to political organizations, and attend political meetings. You also may join and be a member of a political party or club, and sign nominating petitions if you do not identify any of these activities with AmeriCorps*VISTA or your Sponsoring Organization.
Corporation regulations prohibiting electoral and lobbying activities are contained in 45 CFR Part 1226, see Appendix B(?). The approach of the regulations is twofold:
- Restrictions on the assignment of AmeriCorps*VISTA members to, or the receipt of funds by certain organizations because of the nature of the organizations or their activities; and
- Restrictions on member assignments and activities.
The organizational restrictions are based on the premise that the assignment of members or the receipt of Corporation funds by certain organizations (regardless of the proposed assignment or activity of the member) is precluded because of the organization's stated purpose or the nature of its activities.
The restrictions on member assignments and activities contain four basic areas of prohibited activities:
- Voter registration, except that programs assisted under this Act may make voter registration information available to the public on the premises of such programs;
- Voter transportation to the polls; and
- Efforts to influence legislation. The prohibitions are directed to the use of Corporation funds, the assignments of members, and any other activities supported by Corporation funds.
The Domestic Volunteer Service Act provides two exceptions to the prohibition on efforts to influence legislation:
- At the request of a legislative body, committee, or member of a legislative body, and
- Regarding an authorization or appropriation measure directly affecting the operation of the project or program. The regulation, found at 45 CFR Part 1226, describes the conditions under which activities pursuant to these exceptions may be undertaken. The regulation also describes the applicability of the restrictions to Sponsoring Organization employees and the obligations of Sponsoring Organizations to ensure observance of the regulation.
 Justin tried to say that it specifically said in the handbook that members could participate in political campaigns. Obviously not. The important clause here is: "that would result in the identification or apparent identification of the AmeriCorps*VISTA program with such activity" - here in MT, we take a rather strict interpretation that since VISTAs "remain available for service, without regard to regular working hours, at all times during their term of service," any participation may seem to be a part of their service, don't do anything political.
 One of the parts that really bothers Justin - that the Hatch act applies to your off duty hours when serving as a VISTA.
 This sentence might seem to contradict the previous sentence, but one has to note that it's referring to the activities specifically permitted under the Hatch Act (I think see here)
 Note that this list is a subset of the list from the OSC. The others seem to be addressed in 45 CFR 1226, sections 8 and 10. Note that Section 10.12 prohibits members from "Participation in or organizing a political parade" which is what prompted Justin's initial call.
Edit: Fixed the link to the CFR - Hopefully the direct links to sections 8 and 10 will stay good (I'm not sure since they're on akamai . . . )(4/13/2006; 01:13)