Should immigrants be allowed to hold dual citizenship status?

Should immigrants to Ireland be allowed to hold dual citizenship status?

Multiple citizenship, also called dual citizenship is a person's citizenship status, in which a person is concurrently regarded as a citizen of more than one state under the laws of those states. There is no international convention which determines the nationality or citizen status of a person, which is defined exclusively by national laws, which vary and can be inconsistent with each other. Some countries do not permit dual citizenship. Most countries that permit dual citizenship still may not recognize the other citizenship of its nationals within its own territory, for example, in relation to entry into the country, national service, duty to vote, etc.