I am Irish living in Ireland with my English dh. He is considering applying for Irish citizenship so he can retain and EU passport and enjoy the same freedoms me and our kids will still retain post brexit. Am I missing something can non British people, living in Britain and married to a Brit not apply for British citizenship? In Ireland you can after 5 years of marriage you have to pay I think about €500 for it but it is worth the investment.
They can but they have to go through a process first. That includes acquiring Indefinite Leave to Remain/permanent residence: their citizenship applications would fail without it. If you're an EEA national, you get permanent residence automatically if you've been living in the UK abiding by the provisions of the Treaty for 5 years.
According to the British government's interpretation of EU law, which can by no means be assumed to be the right one, in order to get permanent residence if they don't have it already, EEA nationals who have been SAHPs not working, studying etc, needed to have private health insurance. Most didn't, meaning no permanent residence, no entitlement to citizenship, and actually no legal residence in the UK at all. But only if the UK government's interpretation of the need for insurance is right: this is being challenged and has been for ages.
This also doesn't really apply to UK or Irish citizens living in each other's countries, because we have more rights than other EU citizens. We automatically have permanent residence/Indefinite Leave to Remain as soon as we land in the other country. So your DH is in a more advantaged position than other EU citizens in Ireland, and you would be in the UK.