I am an EU citizen currently living in the UK.
On the 29th of March I need to get a flight to Dublin, and I'll come back the 31st.
Is there anything I should be worried about considering that the UK is scheduled to leave the EU exactly on the 29th of March?
I'm going to give a kind of meta answer.
Is there anything I should be worried about considering that the UK is scheduled to leave the EU exactly on the 29th of March
If this is your question, the answer is yes. If at all possible I would avoid flying into or out of the UK in the time directly following Brexit. People will argue that it's going to be fine and others will say it's going to be a disaster but the fact is no one knows right now and that uncertainty should be enough to make you weary and even minor changes to procedure on the British side may result in confusion, delays or an untrained border agent wrongly refusing you.
If I was you I would try to reschedule your trip for 1 month at least after Brexit to allow the dust to settle and to allow new procedures, agreements and training to get sorted out.
The situation is unfortunately unclear.
If the UK's EU withdrawal agreement gets adopted, then 29 March onwards is a transition period and things are basically unchanged from now and there's nothing more to say. But given the current political situation (in particular, that the UK parliament recently rejected said agreement), assume this won't happen unless proven otherwise. Similarly, if the Brexit deadline were to be extended then the UK is still in the EU for a while and things are again unchanged from now, but we don't know if that will happen.
There is a significant risk of planes not flying after March 29 date due to Brexit tearing apart the UK's aviation regulation regime. I don't know whether to say to expect that or not, things may be clearer nearer the date? If you do travel, make sure you have a plan if you're stuck in Ireland.
The settled status scheme for EU nationals is part of the law now, and the test phase of the scheme is open. If you have an EU passport (not ID card, they didn't make the scheme work for those yet) and are willing to pay the fee, you can apply right now. If your application is a simple one and succeeds before that date, then it's very unlikely there'd be anything to worry about insofar as re-entering the UK.
If you don't have it by that date, well, until the law is changed, you still have the right to enter and be in the UK as an EEA national. That change will be carried out a bill currently making its way through parliament, but it's unclear when, because the repeal of the EEA rules by that bill comes into effect at whatever date the government later chooses. However, the government has said it will give EU nationals until the end of 2020 to apply for settled status, so I would expect you won't need special documentation to re-enter in the meantime, but alas I don't know for certain.
Do make sure you have more than 6 months remaining on your passport. They may be more picky after Brexit.
