We have long argued that nonprofit membership organizations ought to have a mechanism in place to screen potential new members to assure that they are a good fit for the organization. Asking for a statement of commitment to your purpose and mission would be helpful in reducing the number of members who don’t subscribe to what you are trying to do.  For a group absolutely intent on sabotaging your purpose, however, it may not be a significant deterrent and you also want to be sure that your bylaws give you a way to expel disruptive or subversive members.

Discrimination is not normally a legal issue for private clubs, and even if it were, political affiliation is not a protected characteristic. You might want to limit membership to only registered Democrats or Independents.

You should be aware that the IRS has concerns about (c)(4) organizations where the “primary” activity is supporting or opposing political candidates.  It has recently denied exemption to an organization it perceived was primarily involved in political campaigns.  The Regulations provide that electioneering is not legitimate “social welfare” activity, so you should be sure that you are spending more of your time supporting ideas and policies rather than candidates.