To my mind, this seems to be the issue:
Many landlords and punters in pub-type venues are not always terribly discerning and therefore the venues will be more than happy to promote just-for-fun or starter bands, as long as they have very little impact on profitability. That's not to say that I believe it's right to devalue musicians and their needs in any musical setting, simply that people being prepared to play for nothing, as is inevitable, will affect pub/club gigs more than others. Many people however, will not be prepared to work NYE at all and that, in addition to larger profit margins and entertainment budgets gives you more room for negotiation in these venues at this time of year.
For those earning a living through music though, the Christmas and NYE break is a busy and demanding time and fees must reflect this, as they do for other service and entertainment industry workers. The most lucrative gigs are, understandably, corporate events and those geared towards musicians.
In answer to the Op's concerns about your bandmates' response to your unwillingness to accept gigs that don't tick the boxes for you, I would be really keen to ensure that everybody's singing from the same sheet regarding the band's purpose - it's very difficult to continue, let alone move forward if you're not.
Incidentally, the 'exposure' argument is, in my opinion, a red herring and can only achieve the opposite of the desired effect. By offering yourself out for nothing with the intention of benefitting in the future, you can contribute to a 'free gig' culture that benefits nobody but the promoter/landlord.
Tobie