Brexit and its implications for British, HU and any other citizens

I've never had any issues with any airlines other than Ryanair and one airline I vow never to fly again with, none of the family will either. My cousin who is a pilot days they are a dreadful company and wouldn't work fir them as they treat their staff badly.

Gosh back in 2019 we landed at the airport in Las Vegas.If anyone has done an 18 hour plus trip then may understand.They advertise a 14 to 18 hour arrival time but do not add the lay over time so your time clock is going bonkers with a min; 24 hour mix up plus the difference in time zones. We were almost the last to leave our flight and for some reason I could not find my passport fast enough.I could Give a àààà and just sat down to dig into my bag to locate it. Right there in the line for passport control. Thinking I am home and all is good, no, all is bad!Triggered Homeland security protocols.The took a every scan known to man on us.I am defo in the system!NWO stuff! - @Marilyn Tassy

You don't need to worry about Homeland Security right now because many of those thugs are not being paid and neither are the wannabe "agents" known as TSA.

It's become rather complicated for dual and triple nationals.  My bro used to enter the UK on his Australian passport simply because he wanted to assert his rights as an Australian.  Those were the days when you didn't need these electronic travel authorisations (ETAs).   

That gets weird as entering and leaving on different passports is now linked in to other paperwork.  Inter-EU it should be fine, just use EU passport.  Outside Schengen gets more complicated.

I really don't know how it's going to work going out of the UK for my kids.  It seems like it could work like this:

Leaving HU

Book Ticket:  Use HU passport details

Check In:  British Passport (therefore no ETA required UK), HU passport ready on standby if need to show if check-in shows HU passport details needed. Check In staff might need evidence of ETA.   

HU passports:  HU passport at e-gates

UK passports:  Enter UK on British passport (complies with new rules)

Leaving UK

Check In:  Show HU passport (therefore no ETIAS needed)

UK passports:  There are no British passport checks leaving the UK

HU passports:  Use HU passport e-gates

(Link) The Dutch don't allow their citizens to retain their Dutch nationality if they voluntarily elect to apply for another country's citizenship; so if my wife applied for UK citizenship, she would lose her Dutch passport. They do permit it if they gain the non-Dutch citizenship through no fault of their own (so in our case, the fact their father was a British citizen means they were British). We had to declare their UK passports when my wife took our trouwboekje to the Dutch Consulate in Düsseldorf to add them to it.
It's never a good idea to use a different passport which you used at check-in, when you get to your destination. It flags up on the flight manifest, which the Immigration staff use at passport control and will at the very least mean more questions and if it happens while something else is going on which has caused extra scrutiny for whatever reason, you can get moved to the interesting persons queue. I only did it once when I tried to jump the queue at IAD by going through the US citizens queue while wearing a British Army uniform, travelling on a NATO travel order and showing my old US passport. I then got into trouble for having half a sandwich and banana in my combat jacket pockets. - @Cynic

Maybe just being open about the different passports is the best idea.   And then you don't need the ETA, ETIAS and blah-blah. I've never known check in personnel to be that diligent on passport checks when there's an actual passport checking desk to airside.

My kids always used HU passports to leave HU and UK passports to enter the UK.  No-one ever said a word about it.

And of course, there are no passport checks leaving the UK.

You could have eaten the sandwich and banana.

I've never had any issues with any airlines other than Ryanair and one airline I vow never to fly again with, none of the family will either. My cousin who is a pilot days they are a dreadful company and wouldn't work fir them as they treat their staff badly. - @SimCityAT

Ryanair I also vowed never to use but I am using them again due to Wizzair withdrawing services to Liverpool.   Their loss. Ryanair has taken up the slack.

I don't like their 737s.  The seats have weird spacing and narrow places at the aisle ends on where to put your feet.  The middle seat has a large space and the window is just normal.  But the aisle under seat space is really narrow.

Wizzair was using Airbus and it's a much nicer plane than the ancient 737 designs Ryanair uses.