Final answer:
The Republic of Ireland is the state that separated from the United Kingdom in the early 1900s, has its own government, and is a member of the United Nations. Scotland also has its own parliament and has had ongoing discussions about independence, especially after Brexit, but it remains part of the UK and is not a UN member state.
Step-by-step explanation:
The state that separated from the United Kingdom in the early 1900s and now has its own government and has become a member of the United Nations is the Republic of Ireland. The Republic of Ireland declared independence from the UK following the Irish War of Independence, resulting in the partition of Ireland and the establishment of the Irish Free State in 1922, which later became the Republic of Ireland.
It matured as a sovereign nation and was admitted to the United Nations in 1955, emphasizing its full independence and acceptance in the international community.
Despite movements within the United Kingdom such as those in Scotland, which has its own parliament and has sought increased autonomy or even independence, the country voted to remain a part of the UK in a 2014 referendum.
Nevertheless, the UK's decision to leave the EU (Brexit) has fueled further discussions about Scottish independence. While Scotland has a measure of devolved power and its own parliament, as of my knowledge cutoff in 2023, it remains part of the United Kingdom and has not achieved the status of a UN member state.