Why don't Irish people befriend foreigners?

OP, I think you're misinterpreting a very significantly large cultural difference as unfriendliness. It's not. It's just different.

Irish culture is quite different to a lot of southern European / middle Eastern and Mediterranean cultures. Socialising does not tend to involve sharing food or bringing people home for meals. There's nothing seen as particularly inhospitable about not doing so, and there are historically very long ingrained reasons for the differences i.e. food/eating here was mostly quite a utilitarian function in the past - most of the population did not eat fancy meals and houses were pretty basic and often very full and busy and in general the idea of bringing people around for dinner was just not a thing, other than maybe amongst the old upper classes.

Irish social culture revolves around public spaces, and mostly the pub, which isn't called a 'public house' for nothing. That's the space that was the living room and the place where people socialised.

If you're not into drinking, and not everyone is, I would strongly suggest that you maybe get involved with group activities that don't involve meeting people at home i.e. join maybe some Meetup groups, get to know people in community groups - there are loads of them from sports, arts, culture, community, Tidy Towns, local committees on all sorts of random topics and they are all generally very open to people dropping in. Just do not expect socialising to revolve around calling into people's homes for meals, and also do not take offence or see it as cold if they do not invite you because it's just not a thing here. It's not that you'll never ever call into other people's houses, but just the contexts are quite different and it's usually more like people you know extremely well and it's often very casual for a cup of tea type of thing, rather than a meal.

Also there are some odd cultural things in Ireland to be ware of (they apply to a degree in parts of England and France too I found). For example, if you offer someone food / drink they'll quite likely refuse it at first, but then be insulted if you don't offer it again. There's a whole 'dance of politenesses' goes on which doesn't necessarily exist in the USA for example, definitely doesn't exist in Germany etc.

Ireland's also extremely casual and informal. So, if you're used to people making a big fuss about greeting you it can seem cold when you just get 'how's it going?' 'grand! yourself?'. Physical greetings like handshaking / kissing are generally not a thing and greetings are often pretty subtle. Again, that does not mean people are being unfriendly or cold, it's just not France, Spain, Turkey etc and the culture around those things are different. On the other side of it, you also might get excitedly bear hugged.

The other issue is you're in a new place and they're at home. So it takes a lot more effort to break into break into very long established social circles, especially in smaller communities where people may know each other since childhood. That's a universal thing. I've lived in several countries and it's not easy to just rock up and meet people.

I know for example when I lived in France, the culture is quite different and I would have had the opposite sense i.e. there was nowhere to meet people. They didn't go to the pub, cafe etc unless very much by appointment, but you learn there are other contexts - clubs, events, markets, organised walking groups all sorts of things and you start to just build from there.

I also lived in Brussels which is an extremely transient and international city and when I was there you'd often get to know someone for a few weeks or months and then they'd be gone. So the result was locals didn't bother with internationals who weren't long term residents as the effort wasn't worth it. So, there's a parallel community of people who are just there for work for a while - busy bars, people going to very EU/intentional focused events and then you've the people who live there full time. It didn't necessarily equate that those were Belgians by birth or anything like that, but it was just that they were the long term community and others were just breezing in and out.

There are all sorts of cultural differences, circumstantial differences and so on to overcome when you move somewhere and they can apply as much in Ireland to someone moving from say Dublin to Cork or whatever. It doesn't necessarily have anything to do with the fact that you're from another country, just that you are not plugged into the networks and are perhaps not understanding quite how they work in a different country.

Yeah that's a big one and also very true of Americans, although they have different 'off limits' areas about smalltalk.

In general in Ireland avoid small talk about money, jobs or trying to be in anyway boastful / anything that might be seem to be boastful (same applies in France actually) whereas in the US dropping in how much you earn seems to be almost acceptable. In Ireland, if you get paid a complement like "oh that's a lovely jumper" just say "ah sure that's just something I found in the press that I bought in Penneys in 1984" Do NOT say "Oh yeah that's my Gucci jumper I spent 2 grand on..." It doesn't impress and above all else DO NOT say "thanks" to a complement. They'll be like "would you look at himself/herself... absolutely full of it! Self-deprecation is the way forward! "Your hair's lovely .." "Really!? You must be mad! I thought it looked shite.. sure I only ran a comb through it!" that kind of thing.

Also having a good old moan about something relatively non-political / inoffensive is often a good point to start off, and has nothing to do with expressing your dissatisfaction / depression. It's just a conversation starter. Whereas if you try that in the US, you'd likely get sent for counselling and antidepressants.

The 'oh so where are you from?' often means ... 'desperately searching for network mode' has been activated i.e. you'll say "I'm from (insert obscure country)" and you'll get "what part?" and they'll go eventually come up with some absolutely ludicrously complicated connection to it i.e. their uncles, sister's brother-in-law's teacher's aunt's dentist's is married to some lad from there.

It's all about learning the nuances of a different culture and they all are quite different in some ways that can be a bit hard to get the hang of. Ireland is by and large very friendly, but it's also an island and has its own quirks that you really do need to learn to navigate.

That also depends on your audience in the US. It gets progressively more open minded the closer you get to the coasts in general (with a few big inland cities being the exceptions).

Knowing your audience is vital everywhere though and also just being aware that different cultures are genuinely .. different. What has worked all your life as your tools for socialising may need to adapt somewhere else. That's part of the fun of travel and living somewhere else though too.

I don't agree that Irish people don't befriend people from overseas, considering my own experience here of knowing loads of people from abroad and a lot of my fiends and family member are even married to people from elsewhere.

I don't think Ireland's all that difficult to socialise in, but you do have to adjust to a culture and a way of doing things that might not be exactly the same as what you're used to.

The other issue I would say is that the last 2 years here have been utterly weird and they've been weird everywhere. I wouldn't base any experience of any country on how things were during the COVID lockdown and restrictions period. We're really only back to semi-normality in the last few months and it will take time for things to fully reestablish themselves. A lot of casual opportunities to network were very limited and it's a particularly profound shock here as our social spaces are all about mingling in busy spaces like bars.