A 501(c)(3) organization can lose its charitable exemption for participating in a political campaign so you are correct in questioning the activity.  The IRS has said that it is not a participation in a political campaign if a candidate rents space or facilities from a charity that is available to the general public and the candidate gets no favorable rate.  (See Ready Reference Page:  “IRS Issues New Guidance on Electioneering”)  It is participation if you deny the same service to other candidates.  Therefore, if you want to sell the advertising space to the candidate who asked, you might want to protect yourself (and generate a little extra income) by specifically offering comparable space to the opposition.

By the way, advertising in your play program is probably generating unrelated business taxable income because the activity is a trade or business “regularly carried on” and unrelated to your theatrical exempt purpose.  Unlike an annual dinner dance program book, which is done only once a year, a program book for every production is considered by the IRS to be regularly carried on.  It may not generate taxable income if substantially all the work is done by volunteers and some of the “ads” may not be taxable if they don’t sell anything, but it is probably an error to tell your advertisers that their payment is a donation to the organization.  (See Ready Reference Page:  ‘Nonprofits Often Worry About UBIT”)