"... take on ..."?
How could there be a conflict? New.net sells .shop.new.net names, ICANN's approved registry would sell .shop names. If people want to mess with their computers by downloading a plug-in to see a different domain system, that's their choice, and theirs nothing ICANN should do about it. Personal freedom: You can choose to see ICANN's .shop, or new.net's .shop.
As far as the ISPs that automatically enable New.net names, it seems logical they would just not renew their contracts with New.net, so all of their customers would default to ICANN's .shop.
The indivdual netizen would still have a choice over which system to use. There would be no conflict. The ISPs would have plenty of time to let existing contracts with New.net expire prior to the release of ICANN's .shop.
Interesting how NetZero, now owned by Verisign, is still a New.net partner. It would be interesting to see how NetZero would handle ICANN's .shop. Would NetZero go for ICANN's .shop? One would have to think so ....