All business owners, wedding or otherwise, should be mindful about publicly identifying their stance on political, religious and social issues. That isn’t to say that taking a public stand is a negative thing; just that, as everything you do in business, your choice should be purposeful, with the consequences in mind.
As an example, in work-related communications (including social media) I choose to keep silent about my religious views, which are probably fairly different from the views of many people I work with in the industry. This is a personal choice. Religion is not something I wish to relate to my career. There are business owners whom I happen to like and refer, who have placed their religious beliefs front and center as part of their business identity — when done consciously, this is something I can respect, even when my own beliefs are different.
On the other hand, I’ve chosen to take a very public stance on certain human rights issues, such as marriage equality, and have mindfully decided to make this issue part of my company’s identity. We recruited only people who believed in marriage equality and began financially contributing to organizations who supported this important issue. We also began the move toward outwardly LGBT-friendly marketing some years back, when it was (sadly) less common than it is now, and we did this purposely: to attract clients who respected every human being’s right to marry, and with full acceptance that we might repel people who did not respect that right. In a nutshell, we didn’t particularly care to work with people who would judge us for our view on this issue.
That’s the thing — when you put your personal views out there, you’re always going to rally support from some people and turn off others. And in some cases, turning certain people off is exactly the right choice for you on a moral/ethical level. Just be mindful, always, of the consequences that a public stance can have, and ensure those consequences align with your values and your business plan.