(1) How do they feel about health care?
In general, supes (short for supernatural) have the ability to regenerate. If they are vampires, they might need to drink blood. If they are werewolves, it will generally happen automatically, unless they've been poisoned with silver or something. If they are witches, they can drink a potion, cast a spell, go to their happy place, etc. In general, supes have limitations that make it difficult for them to hold down a high-paying job with benefits: they might be unable to tolerate sunlight, unable to work for a couple days around the full moon, required to participate at a second's notice in a bunch of illegal Pack related business, etc. In practice, supes who might be able to hold down a high-paying job with benefits don't do so anyway. Either they flunked out of college because they couldn't control their power, or they are Ancient and Very, Very Rich.
Some supes have mortal friends, and they do worry about those mortal friends, especially when they get hurt by being kidnapped or otherwise damaged in a fight. Usually, the solution is to make them drink blood so they heal magically.
There are exceptions (notably in Harris' Stackhouse series, in which somebody winds up in the hospital in almost every single entry), but in general, supes avoid the health care system. When they do interact with it, they're looking for doctors who don't report bullet wounds and they pay cash.
It's not a sure thing, but I'm betting the supes don't have a strong feeling one way or the other about mandatory health insurance coverage for all.
Do supes pay taxes? Well, it seems fairly likely that the uber-rich supes are going to take advantage of their uber-richness to hire good tax lawyers and minimize their tax exposure. The ones not holding down regular jobs may or may not have a strong opinion about taxes, but to the extent that their money worries are severe, they probably would like FICA to be a lot lower. It's unlikely you could hold their attention for long on the subject of tax policy, but they likely have the usual knee-jerk lower-would-be-better response.
(3) Parenting Issues
Supes reproduce. A lot. Which is kind of weird, given how many cross-species couples there are, and how female vampires/werewolves/whatever are supposedly Entirely Extinct and making more is Very, Very Difficult and tends to result in the death of the candidate. It is rarely made clear who delivers these babies, except when the babies are born before the arrival of the skilled birth attendant (like, no one was ever going to show up), or are caught by hubby or the coven or whatever. Usually, babies appear between books (after the romance focused on their parents, and before their parents are the doting parents of 1 or more while a sibling/friend/packmate/coworker/etc. is going through difficulties attempting to hook up) and display many of the characteristics of Soap Opera Children. Could Moms Rising convince some of the women-supes to support their platform of paid maternity leave, affordable high-quality child care, health insurance for all children, etc.? Given how few of the supes have jobs to go back to, and given the above comments on supernatural regeneration/healing, it seems a little unlikely, however, mama's commitment to the rest of the pack/other vampires/etc. does create dilemmas in which she needs someone to watch the kids while she kicks butt (if you know of a SAHD (stay at home dad) supe, I _really_ _fucking_ _want_ _to_ _read_ _that_ _now_. I mean. HAAAAAWWWWT!). Usually, a sibling/coworker/packmate/whatever (who also had her own book at some point in the series) steps up to the plate.
Moms Rising 0.
(4) Peak Oil/Climate Change/Conservation/Energy Security
I've put these all in one bucket, even tho they have slightly different appeal to slightly different groups of people. They all, however, amount to an effort to modify the way that we consume energy (reduction and/or substitution and/or sequestration).
Supes tend to have the capacity to run very fast over long distances including over broken ground in the dark. This limits their need to hop in the car to run to the store (not that we ever actually see a supe hop into a car to go to the store to buy milk or a 6 pack or whatever. Or, for that matter, trot, fly, trace, etc.). I don't know that I've ever read about a supe on a bicycle (that would be damn cool, tho), installing solar panels on the roof, a wind turbine on the estate, converting the limo with the blackened windows to run on biodiesel, etc. And there's a hella lot of airplane travel first class and/or in private jets and/or helicopter. On the one hand, really old supes are really used to not using fossil fuels. On the other hand, they are sucking them down as fast or faster than mere mortals now that they have them.
This does not sound like a Must Reduce Carbon Footprint kinda crowd.
As for what their belief system might be on the subject of extinction, climate change and so forth, I think it's safe to say that people who have direct and regular contact with deities (like, their parents or grandparents or whatever) might have a very different perspective on the relevant science.
Supes in romances have a lot of it, but it is relatively vanilla. Sure there might be a little of the tying up and tying down, and there might be a little doggy style, but it's mostly petting, licking, and tab P slot V action, with the occasional three-some (not all the same gender and almost always with the interactions between the two of the same gender highly limited). For all the interspecies action, there's remarkably little same-sex action, and no species with more than two genders (in romance/supernatural novels published recently by mainstream presses -- I'm sure you can find something out of Ellora's Cave). (I don't know what LKH has gotten up to recently. I'm assuming it's more of the everyone and everything having at the Golden Orifice, but if it got more interesting than that, I'd like to hear about it. And if you don't know what that meant, you don't really want to.).
The major conflict in a lot of supe romances is of the Forbidden Love variety, but some of it is of the They Must Not Know What I Really Am variety (Sookie Stackhouse being a perfect example of that). Eventually, through blackmail, the production of grandchildren, ascending to a throne, abandoning one's past, or whatever, an accommodation is found, but even once the Pack reluctantly accepts that one is sleeping with a Whatever, or the other Vamps have grudgingly accepted that you are doing a Whatever, or you've decided you didn't like your Coven after all, or you want to Effect Change from Within, there is still a huge chunk of prejudice against your mate floating around. And you tend to become friends with other people after they wind up in the same situation.
Why do I feel like this stuff is aimed squarely at readers whose extended family and kinship network (at least the one they were born into) is so conservative it's basically safe to call them bigots, but of course no one will because they are Family?
And I think I should be a lot more grateful to Charlaine Harris and her Sookie Stackhouse than I often feel. Her political world is way sophisticated compared to most of the rest of what is out there.