Quantum mechanics requires a vacuum energy 40 orders of magnitude higher than that indicated by cosmological observations. Which side is most likely to be right,& when the truth is finally established beyond doubt,as one day it will be,won't this be extremely embarrassing for whichever group turns out to be wrong? Forty orders of magnitude is not a trivial error.
I'm not sure the language of "sides" really applies here. There is a model, one of the predictions seems to be wrong, so we will try to find a better model.
By way of analogy, look at the model of black-body radiation developed in the 19th century, one of its predictions was that an infinite amount of energy should be radiated at very short wavelengths. That prediction was ridiculous, so over the early part of the 20th century, people developed a better model, that "better model" became known as quantum mechanics.
There's nothing embarrassing about a model being wrong. All models are wrong, buts some are more useful than others. QM is a very useful model of reality in many many situations but seems to give some surprising values. So physicists try to find something better. There aren't "groups". This isn't a school playground. Being wrong isn't embarrassing, it just means the theories (or the observations) are incomplete.