¡Dios mio!
 

Is this phrase considered offensive by any Spanish-speaking cultures or subcultures?

Despite the widespread usage of "Oh my God!" on the Internet (omg) and in other casual settings, there are some people who believe using a phrase like this is akin to "taking the lord's name in vain." Some will change it to "Oh my gosh!" or use even more innocuous phrases like "Goodness gracious!"

Are some people similarly offended by "¡Dios mío!, and if so, are there softer phrases one can use for the same effect?

It's pretty common, but you can say ¡ay, ay, ay! or ¡diablos! ¡miércoles!, madre mía. Religious fanatics will always find something to be offended by, so some of those terms may be profane as well. With luck no heads will roll.

No, men, its not offensive for general poblation, its as says "OMG", "DAMN", "WTF", its the same term.