What if we are looking for the wrong signs of life on other planets?
Are there any fields of astronomy that look beyond the "near-Earth"
life comparisons and look for life in other (drastically different)
I'm always bothered by these reports because they are all predicated
on the premise that life on other planets will closely resemble our
It doesn't matter what people think. What matters is what we can observe. Just because they will probably look for life on Earthlike planets first, doesn't mean they won't look elsewhere. The answer will depend on what they find, not what anyone expects to find.
I think there are a lot of good comments below your question, but I want to try to address a few points.
On looking for life.
The scientists that look into space through our biggest telescopes aren't exactly "looking" for life on other planets because life is too hard to see. Mostly, they look at stars. Our best telescopes today can't see exoplanets at all. Exoplanets are detected indirectly by variations in the stars they orbit. If exoplanets are too far away most of the time to even be seen, looking for signs of life on them is obviously out of reach. We're not actively looking for life because we can't. We need much bigger telescopes for that.
So, basically "20 Earthlike planets discovered" is the upper limit of our technology right now. That's today's cutting edge discovery. I understand that it might be boring. I know that they're just adding more planets to the directory, but that's the limit that our best equipment can deliver right now.
Almost nothing is known about all those planets, just the very basics, like how close they are to their star, and about how large they are and sometimes, about how dense they are giving us a limited idea of their composition and if they are hot, cold or perhaps in the Goldilocks zone. If there's only 5 lines of data per exoplanet, the tag-line "Earth-like" often makes the best headline, not because NASA is focused on only Earthlike planets, but because there's not a lot of detail.
It's kind of like "I see a bird, but it's far away and I don't have my binoculars. It's flying south", but I can't see what kind of bird, I can make out the size, to some extent, I can see that there's just one, but I can't make out the shape. So, I write in my bird journal "One largeish bird flying south - too far away to see what kind".
That's basically where we stand with exoplanet observation right now.
This will change some when the James Webb Space Telescope is operating. The JWST should be able to see star-light filtered through some exoplanet atmospheres, which will tell us a whole lot more than we currently know about some of those exoplanets. Information such as how thick an atmosphere and what it's made of will tell us a lot, and give us some information on the climate of the planet. JWST will be a HUGE (all caps for emphasis) step forward in the search for alien life, though it still won't observe life directly, but it will hopefully get a good read on some exoplanet's atmospheres, and from that, deductions can be made, such as abundant oxygen isn't expected without some form of photosynthesis. Oxygen is too reactive to be likely to exist on it's own.
A combination of CH4 and O2 could be especially interesting and one of the first things to look for, but they also have to be careful. There's always the chance of more than one explanation for a planet's atmosphere. We shouldn't expect any kind of guarantee of discovery, but JWST should be an enormous step forward in what we can observe about exoplanets.
Scientists in this field, their job is essentially to analyze and report the data. Their job is not, for the most part, to speculate on life but to simply report what can be verified (and today, relatively little other than "I found a planet" can be verified).
Theoretical biology is great. Don't get me wrong. It's fun and it's real science, but the majority of telescope observation focuses on observe, analyze and report. That might sound dry, but that's mostly how science works. "20 Earthlike planets found" was impossible 10-15 years ago. It really is cutting edge.
On Theoretical Alien Life:
Scientists, today (Neil deGrass Tyson among them) who would love to get a closer look at some of the Moons of Jupiter and Saturn, because they are thought to hold the best chance of having life beyond Earth in our solar-system. The desire to find alien life, if it's out there, is one of the highest held goals of NASA and Scientists in this field. Nobody's ignoring or dismissing anything. They will likely point JWST towards Earthlike planets first, but that's only natural.
I'd like to also point a basic rule of astronomical observation. "Weird" is actually good. Weird leads to discoveries like dark matter and dark energy. Like the Isaac Asimov "That's funny" quote, finding things they don't expect is often the best find. Scientists love that. If weird atmospheres are found by JWST, it won't matter if they are on Earthlike planets or not. Anything weird or unexpected will be of great interest and closely looked at.
Like those theoretical Alien Mega-structure or Dyson sphere stars (which probably aren't Dyson spheres). I'm highly skeptical that it's aliens, but I'm glad they're looking into it. Anything unexpected is worth studying.
When JWST starts to get better data on atmospheres, then you'll see more interesting headlines than "Earthlike". For now, and for the next year or so, "More Earthlike planets found", is as far as our technology can take us.
Finally, I want to point out that on theoretical biology, there are issues. (The other answer covers this better than I did so I'll abbreviate), but there are reasons to suspect that life might need to be carbon and liquid water based, so planets thought to have liquid water should be the first places to look.
And ultimately, it doesn't matter what people think is out there. What matters is what JWST (and telescopes that follow) will discover. What we know about the Universe is based on what has been observed, not on the various prejudices and assumptions people made. Sometimes what is observed goes against the scientific belief of the day, and that's what's great about science. Evidence trumps belief.