The first amendment in the US constitution grants everyone the freedom of speech, press, religion, assembly, and petitioning. Preventing churches and other tax-exempt organizations from organizing politically outright robs them of their freedom of assembly, which the first amendment protects. Thus, if you politically silence religious and tax-exempt organizations, you are going against the law of the land in the US by attacking a group's first amendment right to freedom of assembly.
As Americans, we live in a society where we have the gift of free speech. This should not be taken away from churches and non-profit groups, who often do have political stances. Supporters of churches and tax-exempt organizations often will donate funds if they agree with the group's mission and purpose. These groups should have the right to organize around political issues that they are passionate about so their supporters know they are working towards making a difference.
Churches and tax-exempt organizations should be allowed to politically organize. Political speech is free speech, which is protected under the First Amendment. Not to mention, citizens have the right to peaceably assemble together. Therefore, the government should not put restrictions on what an organization decides to do to support a political cause or campaign.
We live in a free country. People should be allowed to peacefully do whatever they would like to. Now, a Catholic priest, for example, I know should not voice his political opinion from the pulpit, however, there are no such restrictions for the regular lay person. People can believe what they want and organize politically if they want.
IRS Tax Code 501(c)(3) requires that a tax-exempt religious organization “may not attempt to influence legislation as a substantial part of its activities and it may not participate at all in campaign activity for or against political
Basically, if they do attempt to influence political matters they should have their tax exempt status revoked.
Members should not be prohibited from independently politically organizing, but non-profit and other tax exempt organizations should not promote political candidates or campaigns. This goes against the principles behind having a tax exempt status. There is no reason why they should not support causes, however it is important that they do not force their members to vote a certain way.