R6RS requires that (max +inf.0 x) for any real x return +inf.0; it is silent about (max x +inf.0), but I'd think that was entailed. I tested (max +inf.0 +nan.0) against the test suite.
Racket, Gauche, MIT, Chicken (with and without the numbers egg), Scheme48, Guile, Ypsilon, Mosh, IronScheme, STklos, Elk, VX return +inf.0.
Gambit, Bigloo, Kawa, SISC, Chibi, Chez, Vicare, Larceny, NexJ, UMB, Spark, Femtolisp return +nan.0.
My other Schemes throw errors, either because they don't like inexact numbers, they don't like division by 0.0, or they produce cockeyed values of (/ 1.0 0.0) and/or (/ 0.0 0.0).
Note that the six R6RS implementations are split 3-3 (or 4-3 if Guile, which does not fully implement R6RS, is included), and that all the Java ones prefer +nan.0, as Java does.