Well of course I have to wade in from the
other camp, for many reasons, the first being that from experiential events, I know it's not only possible, but the true way of things.
I've connected to animals (and even people) myself, and discovered I'd been pretty darn accurate -- the last time, with a bunny I'd just written about here elsewhere. In that instance, the bunny connected with
me first, w/o me even asking for it, and according to the guardian (also a colleague of mine), I was about 80-85% accurate about the info./insight I received w/i a few, short minutes. It was effortless.
I've also connected with a horse spontaneously, too, during an An. Comm. class, but again, I hadn't even been going through the rote protocol when this happened, and the horse gave me some info. that I couldn't possibly have known about (esp. since I know little about horse stuff, body parts, etc.), and once again, the guardian confirmed that the info. was definitely correct.
But more than this, I did this naturally all through my
own kidlets' lives, in numerous ways that were just.....
natural to me, to that innate intuitive sense that is a part of ALL of us. THEY are the ones who taught me this in more detail and consistency. It works both ways, of course, as well. Sabin used to 'hear' my worried mental calls for him and show up from wherever he'd been w/i just a few minutes.....ALL the time. I experimented with this and found a common denominator -- my heart had to be TRULY engaged (in this particular case, truly worried or anxious!) and open, or he either wouldn't 'hear' me or just wouldn't respond (not sure which of the 2 was really happening, but ONE of them anyway) And that's just one example. There were many, many more, with both him and Nissa.
And as they correctly say, most people have had experiences of this, too, with other PEOPLE, like when you think about someone and suddenly they call you on the phone, or when you're able to finish someone's sentence for them, as just 2 tiny examples. As part of another ACing course I took long ago, we also did exercises where one person thought of a colour and the other had to sense what colour that was. For myself, I never got the colour WRONG, not even once. Then I tried it with my H later and even w/o the whole preamble, it still worked accurately for me. His results in sensing MY colour weren't as good, but then he wasn't really and truly all that interested. So, our willingness to be open also plays a huge factor.
When someone doesn't believe it's possible, it is really driven by the minimum of a subconscious belief in separation, a belief that we couldn't possibly all be One, or connected. It is a belief in the solidity of matter and a disbelief in all that the 'new' sciences (those that are already about 50 yrs. old and newer but haven't yet been allowed into mainstream teachings in any significant way) have discovered about how our universe REALLY works, and what it's REALLY composed of..... far too large a subject to cover in a short space, but in a nutshell, a most definite SHARED CONSCIOUSNESS that is the
driving force behind absolutely EVERYTHING 'out there'. It's not really 'out there' at all, as it's part of all of us, WITHIN us, as we are not separated whatsoever from even the most distance particle across the universe. What we think, and especially what we feel, is immediately reflected in other particles, no matter where they are. These are now proven facts, not just airy-fairy la-la-land flowery, poetic writings. But as I said, it's far too large a subject to cover in just one paragraph. It does, however, also explain quite eloquently how distant &/or energy-type healing works, too. It's rather MORE impossible that it wouldn't. There is no separation, no distance, and no time-space between us or anything else 'out there,' is what it boils down to.
I've posted many times here and on many subjects that relate to all this, but it's up to each one to either take it in, investigate it further, or choose to remain locked into paradigms (world views) of centuries past.
That said, for ACers themselves, just like with any other profession, there are good/better/best ones, as well as out-and-out charlatans....and even the latter may indeed get some things right some of the time because of that factual connection to All That Is, despite their own "faking it"!

The trick is always to find one who doesn't speak ONLY in general terms, but gives you more concrete "validations" that at least certain parts of the info. is correct, so that you can trust in the rest that sounds more 'general.'
For just one example, Irene Lane gave me specific and unsolicited info. from my gal related to a sudden and inexplicable acute illness she'd gotten once, where I
hadn't even asked any question about it yet, but she referred to some details about it that had, indeed, happened, and proceeded to tell me that is WASN'T the particular beef food (it was beef baby food) we'd fed her that had made her vomit, but something else. She'd had no idea whatsoever that she'd been ill in this exact way, nor that we'd fed her that certain food, nor that I'd been suspecting that food itself (because I discovered it had lemon jce. added) for her stomach upset. Yet, Nissa relayed to her that info. and even interrupted our conversation/reading in the middle of something else to 'shout' out, "Tell her it wasn't the FOOD that made me throw up!" Then the details came out AFTERWARDS. Since I've always tried to word my questions to ACers in such a way that they can't really tell on the surface what I'm really after for validation, that's one thing, but this was entirely another matter because I hadn't even GOTTEN to the part where I was going to begin asking questions about her illness, so Irene didn't even know she was ill. And again, this is just one example of many.
Almost everyone has had instances of what they could call ESP (perhaps think back to your childhood or teenhood for examples), but if we consistently choose to try and explain away those events as mere coincidence, then guess what? We're not going to believe them no matter HOW compelling the evidence really is. That's your subconscious programming. But for myself, after delving into such related things for so many years now already, to me, this is Kindergarten in a way, as it's all become such a GIVEN to me, I can barely even remember when I
didn't believe it.