I don't think "neutral" is quite the right word for the audience in question. It may be the best one, but there is more to it, as it only captures the group's view of itself, and not how others might see it.

The Bayesians (vegetarians) see the "neutrals" (omnivores) as non-understanding (animal-killers). The neutrals see themselves as partaking of the best tools (foods) there are, both Bayesian and frequentist (vegetable and animal), and think that when Bayesians call them "non-Bayesians" (animal-killers) the Bayesians are making a mistake of fact by thinking that they are frequentists (carnivores). Sometimes Bayesians even say "frequentist" when context makes it obvious they mean "non-Bayesian" (or that they are making a silly mistake, which is what the threatened "neutrals" are motivated to assume).

As neutrals is absolutely how those in the group in question see themselves, but also true is that Bayesians see them as heretics, (murderers of Bambi, Thumper, and Lambchop), or what have you, without them making a mistake of fact. The Bayesian theoretical criticisms should not be brushed aside on the grounds that they are out of touch with how things are done, and do not understand that it that most use all available tools (are omnivorous). They can be addressed by invoking the outside view against the inside view, or practice against theory, etc. (these are arguments in which Bayesians and frequentists are joined against neutrals) and subsequently (if the "neutrals" (omnivores) do not win against the Bayesians [and their frequentist allies {those favoring pure diets}] outright in that round) on the well worn Bayesian (vegetarian) v. frequentist (carnivore) battlegrounds.