I have seen red tails a few times riding my horse about a mile east of my house, and a neighbor a half mile to the west has told me she sees them hunting in her field. I had never seen one right by our house before but clearly they summer in the vicinity.
Last fall or early winter I lost a pigeon definitely to a hawk (I found the remains, and have posted about it here) and another one disappeared. At the time I checked range maps and the red tail’s official winter range comes up to Massachusetts or southern New Hampshire, not as far north as we are, but with the mild winters we’ve been having I would not be surprised if they are sticking around. Or at the least they may delay heading south until the snow actually sticks, which seems later every year.
I am quite fond of our summer resident Broadwinged hawks, which I can hear nearly any day in the summer and see almost as often. They are so much smaller and don’t seem to bother either chickens or pigeons. I know they sometimes can but so far they haven’t. I think we have enough small mammals, particularly chipmunks, to keep them fed! We seem to start having problems after they head south for the winter.
I’m in the general vicinity of that area and below is my ranking of the local raptors, beware of armchair ornithology:
Broad winged hawks (BWH) are the best. Like you said they technically could, but I’ve never had an issue with them and my pigeons and the neighbor tells me the same for the chicken, guinea, and peafowl chicks that he has. I say they’re the best because if you get a breeding pair in the area they’re likely to harass other hawks. The only downside to them is that they’re summer visitors only!
Red shouldered hawks (RSH) are the second best. Same with the BWH, they technically could predate on a pigeon but they seem unwilling. There is a breeding pair in the area, I’ve posted photos way back in this thread of the female hunting from the flagpole in my yard for chipmunks and ignoring the pigeons nearby. They’re big soar-and-screamers like the BWH, and are also liable to drive other raptors from the area if you have a breeding pair nearby. They might eat domestic poultry, after all they are generalist opportunistic predators that eat anything from bugs to crayfish to rabbits, but I’ve never seen one even attempt to catch a songbird, dove, etc
Red tailed hawks (RTH) in my experience will try to catch pigeons but they are very unsuited. They’d take a fancy breed that can’t fly, but are no match for the average flying pigeon. They’re the largest hawk in the east and will also drive other species away from a nesting territory. Certainly a hazard to poultry.
Worst of all hawks for pigeons in eastern NA is the Cooper’s hawk, which is a bird-eating specialist. Fast as a bullet and very agile, they can grab songbirds at feeders or take doves, pigeons, sparrows, parakeets, and any other introduced species. The dove family (and probably the extinct passenger pigeon) make up a huge component of their diet, and they’ve also undergone a massive range/population expansion, benefiting from human development. This hawk thrives in dense forests, farmland, city blocks, and suburbs. They’re everywhere, and will definitely cull your weakest flock members. They’re quick but can’t take pigeons in the open, the pigeons just outclass them in overall speed, endurance, and ability to gain altitude. They usually ambush from foliage, and if they aren’t successful will follow the pigeons way up into the air before they eventually give up. They have a big long tail which gives them a cross shaped silhouette.
The Northern goshawk is just like the Cooper’s hawk but bigger, and a resident of undisturbed forests. They’re not very common.
Woe be to your pigeons if there are peregrine falcons in the area. In the Northeast they are not yet common outside of the cities where they nest like New York, Providence, and Boston. I’ve lost a few pigeons to them where I am but fortunately those were not resident falcons and I didn’t see them again. Kestrels are a small and harmless falcon.
All the hawks and falcons above are migratory to an extent, with variation between migration and year round residency even within the same species. Young hawks leave their natal territories and are more migratory, and often are more likely to attack domestic birds due to inexperience or desperation.
I agree

I would treat them for parasites immediately though, I’ve acquired lost birds or purchased birds from a variety of sources from reputable racers to backyard hobbyists and every one of them has had pigeon lice, no mites thankfully.