If you intend to host your service behind something like CloudFlair it doesn't matter that some users don't have IPv6 yet: they'll contact the cache service via IPv4 and it'll contact your servers as needed via IPv6. The end user doesn't have to care, or even know at all, and you have just made a saving by not having to pay for IPv4 addresses.
People will start to care when IPv6 takeup hits critical mass and we start seeing services optimised for it. When people start seeing services they want to use not working as well through layers of NAT, they start asking their ISPs why they are having a problem and their friends on other ISPs aren't. Maybe at some point services will start charging a premium for IPv4 access (so IPv6 users aren't subsidising those who haven't moved forward yet) like on retail business did for IE6/7 users (http://www.bbc.co.uk/news/technology-18440979) then people will care. That seems extreme though and might alienate users, less severe option would be to serve more adverts.
There are some places where things are already heading towards being IPv6 only. A friend of mine noticed this when out east for a work related trip, the hotel he was in provided Internet access but IPv6 only internally. They provided a 6-to-4 gateway so IPv4 only sites worked fine (with everyone from several places looking to be coming from the same address) but your device had to speak IPv6 to connect to the network in the first place (which his phone didn't).
I'm just waiting for when we get to the point where there are thousands of users behind the same ipv4 address and one of them gets the ip banned from something popular. I'm sure customers would start caring then.
Or worse, someone does something incredibly wrong from that address (arranges a bombing, posts kiddy porn, or so forth) and the police arrest everybody associated with the address just-in-case...
People will start to care when IPv6 takeup hits critical mass and we start seeing services optimised for it. When people start seeing services they want to use not working as well through layers of NAT, they start asking their ISPs why they are having a problem and their friends on other ISPs aren't. Maybe at some point services will start charging a premium for IPv4 access (so IPv6 users aren't subsidising those who haven't moved forward yet) like on retail business did for IE6/7 users (http://www.bbc.co.uk/news/technology-18440979) then people will care. That seems extreme though and might alienate users, less severe option would be to serve more adverts.
There are some places where things are already heading towards being IPv6 only. A friend of mine noticed this when out east for a work related trip, the hotel he was in provided Internet access but IPv6 only internally. They provided a 6-to-4 gateway so IPv4 only sites worked fine (with everyone from several places looking to be coming from the same address) but your device had to speak IPv6 to connect to the network in the first place (which his phone didn't).