you got that wrong my friend, if the miners switch to the new client, exchanges wont have any other choice but to follow, because the old chain will be dead..
Not really, because new miners can jump in and resurrect the old chain. There was a recent case of an altcoin, I don't remember which one, which tried to hard fork but couldn't because the one exchange it traded on stubbornly refused to go along.
That might be an issue for a small network, where one player may have the power to do so, but as Phil Potter from Bitfinex said, "we will see what our competitors are doing, if there is a consensus, we will follow it'
tl;dr This is not about taking sides, its about following the money.
It doesn't matter if it's one player or a consensus of players; the result is the same. If there is consensus among exchanges to stay on Core, then Core will win, no matter what miners do.
XT'ers shouldn't be lobbying miners directly. They should first lobby the node operators, then the exchanges and payment processors. If they win those two battles the miners will follow.