How far should the state stick its nose?

Someone claimed that because there is a halakhic prohibition against marrying a non-Jew
Therefore, the state’s role is to find out exactly who a halakhic Jew is, so that we do not fall foul of a halakhic prohibition.
Although the result could be aggravation according to extremist views, this is the role of the state.

I saw in the Shulchan Arba that it is forbidden to marry a forced laborer or a family of forced laborers.
Is it the state’s job to thoroughly investigate who is subject to halakhic law, so that we do not fall foul of a halakhic prohibition?
Although the result could be aggravation according to extremist views, is this the role of the state’s poor?

Another alternative is that everyone should ask their rabbi who exactly is Jewish enough and to what extent is he subject to a full or family of enforcers? Isn’t this the state’s job?