One of the key features of the Ethereum blockchain is that it's an open, global infrastructure, and so with MoonCats being part of that, third-party developers can easily integrate with MoonCats, and build applications that can detect whether the visitor is a MoonCat owner or not.
The original MoonCatRescue project was launched before NFT standards were finalized, but ponderware has created a "wrapping" contract known as the Acclimator that makes them ERC721 compliant, so tools and libraries that know how to interact with ERC721s should be able to interact with Acclimated MoonCats without special configuration. The contract can be found here: 0xc3f733ca98E0daD0386979Eb96fb1722A1A05E69
For more detailed information about integrating, and the deeper technical workings of how the MoonCat contracts work, and the different traits of MoonCats, read on!