Airline pilot here …
In general in the airline industry there is NO premium pay for holidays, and only trivial premium pay, if any, for night/weekend/3rd shift work. At least that’s true for pilots & flight attendants. Unionized ground staff have a greater likelihood of some premium pay for some things.
Having major holidays off is, in general, very popular and you have to be fairly senior to get Christmas or Thanksgiving off. Groundhog Day or President’s Day less so.
The fallacy in the OP’s question is in the details of seniority. Speaking just to pilots:
A typical big airline flies 5 or more types of aircraft. Each aircraft has 2 crew positions. That means there are ten separate jobs at the airline, all of which are “pilot”. The distribution of jobs follows seniority, but people only change jobs every few years.
An individual pilot starts out as First Officer on the smallest, lowest paying airplane and (with luck) moves up in aircraft size & pay, then eventually over to the Captain’s position on the smallest, lowest paying airplane, then (with luck) moves up to the larger and larger aircraft until mandatory retirement cuts off his/her career. So in 30-ish years he/she may hold only 6 or 8 different jobs total.
Looking at a hypothetical airline … say you’ve got 50 very senior guys who fly, say, 777 Captain. Then you’ve got another 100 almost-as-senior guys who fly the 767 as Captain. Then 200 757 Captains, then 400 737 Captains, then you get to the First Officers (co-pilots). Again we have about the same numbers: 50 777 F/Os, 100 767 F/Os, 200 757 F/Os, and 400 737 F/Os.
That’s 1500 guys (and probably 25 gals), enough for a decent sized airline. There are a bunch of details I’m leaving out, but this is a pretty good sketch of how an airline is staffed.
Now it’s time to decide who works Christmas. About 1/2 the people are working any given day.
So the top 25 of the 50 777 captains take Xmas off, and the next 25 work. These guys are very, very senior in an absolute sense, but are junior amongst the 777 Captains. They fly the crappy trips on the crappy days.
Now we have to crew the 767 operation. Guess what, the top 50 take Xmas off, and the bottom 50 work. Those are still some damn senior guys, but they’re doing the transcon redeye (which torture ought to be against the Geneva Convention) every Saturday night / Sunday morning while the senior guys do the banker’s hours ORD-LAX & back day trip on Tue-Thu.
Even among carriers that only fly one aircraft type and therefore only have 2 jobs, not 10, you still have the effect that the juniormost Captain out there is roughly 1/2 way up the seniority list and has been doing the job for quite awhile. And even though the bottom-most, least experienced First Officer is working XMas, so is the F/O almost halfway up the F/O ladder, i.e. 1/4 way up the total career ladder.
So amongst pilots the idea that only the newbies are working XMas is definitely faulty.
Conversely, most carriers do not segregate their flight attendants by aircraft type. They may segregate between international and domestic, but that’s about it. So on Xmas you’ll definitely see fewer dinosaurs and more young’uns. Although now that the carriers are hiring a lot of mid/late-40s ex-wives as F/As, age is no longer the reliable proxy for seniority it once was. Back in the 60s it was common for F/A hiring standards to be between age 20 and 22 only.
Finally, as to accident rate … the US airline industry only wrecks a handful of airplanes a year; how would you expect to see a difference in accident rate between, say, the 5 major holidays and the rest of the year when it’d take a couple hundred years to get a decent sample size?
So, no, in my humble (but professional) opinion, there is not a difference in safety between holiday and non-holiday air travel.
If the statistics somehow proved me wrong, I’d expect the majority of the difference to be attributable to worse weather agross the Big 3 holidays, T-Day, XMas, and NY, and/or additional psychological / emotional distraction leading to reduced crew / controller performance, rather than to seniority/juniority. There are provably more divorces, deaths, and suicides during the heavy Holiday season. Crewmembers are’t immune to the same emotional pressures.