Q: I work at my church and we switched to Media Shout but I need to open in my Mac. Can I?

They have a Mac version but according to their website it does not have all of the features of the current Windows version and it isn't compatible with the current Mac operating system (OS X 10.11 El Capitan): http://www.mediashout.com/item/mediashout-mac

The usual way to run Windows programs on a Mac involves buying (licensing) a copy of the Windows operating system and installing it either in 1) Bootcamp https://www.apple.com/support/bootcamp/ or 2) using virtualization to install Windows (one example: http://www.parallels.com/products/desktop/ )

To share the screen on the remote system...

Apple Remote Desktop is a commercial program, and with far more capabilities than you will want or need, here.

The (free) CoRD VNC/RDP remote screen-sharing application will allow screen-sharing with a properly-configured Microsoft Windows box.

Beyond the screen sharing application, you will need to have either a virtual private network (VPN) connection to the church, or to have enabled a mechanism known as port forwarding, as a typical network will (correctly) block this access without manual overrides within the church network configuration.

Opening up ports means that everybody on the internet can try to access and attack and load your Windows system with malware and otherwise compromise both that system and other systems using it.  Without appropriate security, opening ports into any network and any computer is a Bad Idea.

A VPN either requires getting a VPN server going within Microsoft Windows or acquiring and configuring a VPN server in a firewall — the existing gateway box here almost certainly lacks a VPN server.  Setting up a VPN server in a gateway box or in a Windows box probably isn't the best fodder for discussion around here, either.

Per the FAQ, the purchase includes licenses for three systems.   Load it onto a local Windows system, and learn it there?   Or the Mac client, if there is one.

Given the questions you're asking, networking and VPNs are probably more complexity than you'll want here.   This is a fairly complex configuration, if you're not already comfortable with IP networking and network security.   I'd very seriously avoid opening up the church computers to unrestricted remote access, too.  More than a few church servers have been breached, and that ends badly for the computer, for the computers of other folks accessing the church servers, and the church.