I grew up and lived my whole life in Lakewood. This has not been a thing since back to the last years of the rebbes life. Honestly, nobody cares about having "the fight against Lubavitch". It's a non issue and has been so for the last 25 years or so.
That's not what I heard from a semi-Heimish non-lubavitcher lakewood friend (I've heard from lubavitcher friends in lakewood too, but if the nonlubavitch ones get cheppered about it b/c they're "heimish", what does that tell you?). He said there are still a few yeshivish rebbeim and maggidei shiur for his kids that will knock lubavitch in front of the whole shiur. Yes, when there's antagonism in Lakewood it's only overwhelmingly "only" "soft antagonism" not "hard antagonism" from what I've heard and BH it's seemingly getting much better, but let's not kid ourselves, there's still a way to go and it's not a one way street.