I like the idea of assuming that this may have been done in error -- Either someone at the church didn't realize that the bulletin board was PTO "space'' or some other oversight took place. Let's hope so, anyway!
It does make sense to request that the poster be taken down.
Otherwise, this could open up a whole can of worms, as they say, because it advocates for a particular political position.
The PTO may not have had anything to do with the poster. As you hold your preschool in a church, a member of the church may have placed the poster there under the assumption that parents with kids in the preschool may be concerned about issues that church members find important. Our school rents from a church as well and we sometimes have church material posted on our boards. I think people just try to get their information out wherever they can. Maybe a sign on your board that states something along the lines of please obtain PTO approval before posting.
If I were in your shoes, I would politely tell the current board about it (they may not have noticed) and ask them to take it down. If there is any resistance, you could point out that such a poster could violate IRS rules regarding political activity by nonprofit organizations. See www.nonprofitlawblog.com/home/2006/02/irs_investigati.html for details.
I started the PTO at my child's school and served as Chair for three years. My term ended this past year. I still have a child that attends school there. Our preschool is housed within a church but in not religiously-affiliated. Today, I saw that someone had posted a poster of the Reverend Billy Graham with a quote to encourage others to vote to protect the "biblical definition of marriage" and the "sanctity of life" on our PTO bulletin board. (In the past, we had reserved a section of the board for miscellaneous, non-PTO messages, but this year, the leadership team eliminated that since there is adequate space throughout the building for other groups' posters.)
This poster make it appear as if the PTO is taking a religiously-oriented political position and encouraging parents to vote a certain way. I am furious! I was inclined to remove the poster, but I am no longer a board member. Should I contact the current board and school director to notify them that this poster is completely inappropriate and ask them to remove it or should I simply remove it myself and inform them that I did?