Personally, I use the British spelling for "Theatre" and "Saviour" for no other reason than I prefer how they look over the American spelling.

Americans sometimes use the British spelling to make something seem fancier or more exotic. The predominant spelling is with the ter ending though.

It looks fancy. Really, that's it. Some people think "theatre" looks better than "theater," fancier, more sophisticated, older. So, when certain groups choose a name for their building (or for their group), they go with the British spelling. You will also see "Centre" from time to time in the US for the same reason.

Spelling differences between the US and the UK can be less absolute than people think. Often the supposedly "British" spelling is simply a less frequent US spelling. One example is "traveller," which is spelled with two ll's in the UK. In the US it is usually spelled with either one l, following Noah Webster's lead--but two l's are seen and don't look "wrong" to my eye. As I type this right now, my computer is putting a squiggly red underline under "colour," but not "traveller." General Lee (the great Confederate general in the American Civil War of 1861-4) had a horse named "Traveller," always spelled with two l's. Usually (but not always) we write "movie theater," as well as "operating theater" (in a hospital) or "theater of operations" (military). However, we usually use the "theatre" spelling for the names of theatres that present live stage productions, and for the theatre arts. For example, Emerson College in Boston offers undergraduate programs in "Theatre & Performance," "Musical Theatre," and "Theatre Design/Technology." It also operates the "Emerson Majestic Theatre." Fancy or serious movie theaters may call themselves "cinemas" or "theatres." Another example of a supposedly British spelling in the United States is provided by the village of Newton Centre, Massachusetts. Notice that this is the official, correct, legal name of the village.

This is amusing: http://www.nytix.com/Links/Broadway/listofcurrenttheatres.html This is supposed to be a complete list of Broadway theatres, and every one of the forty-one spells its name "theatre." However, the "Al Hirschfeld Theatre" is managed by "Jujamcyn Theaters." And all of the "theatre notes" in the table use the spelling "theater" when it is not part of a proper name. Thus, the notes on the "Belasco Theatre" say "Broadway mogul David Belasco built this theater and named it after himself."