Party Mode or guest Access for Google Play Music?
There is a way to share songs and albums with friends and family. This is not quite the same as a "party mode," but is the closest thing I have found to it.

Pros: 
1. Don't need to give anyone your account information. 
2. Friends can listen to shared music on any device they want.

Cons: 
1. Only works with Google+ (for now) so your friend must have a device which can access Google+. 
2. Can listen to the entire song only once for free. 
3. Only works with limited number of songs (many more are being added though).

Setting up a type of "guest account" may be a viable option but this opens up a whole hose of security concerns - I doubt Google would implement this officially. Sharing music has a long history of abuse.

So much music can be found for free these days, sharing a listing of your favorite songs may be all that is necessary.