Is H2CO3 (carbonic acid) soluble or insoluble in water?
Yes, it is soluble.

For example, the oceans are constantly getting $\ce{CO2}$ from the atmosphere that gets converted into carbonic acid and thus decreasing pH on a global scale. Or the soft drinks we drink contain carbonic acid in them in dissolved form only due to mixing of $\ce{CO2}$ gas.

Also, not all carbonates are insoluble as Ben Norris has commented.

Hard and fast 'rules' in chemistry tend to be rare.  Consider them guidelines.