There are at least two scenarios.
Israel, Mexico and other countries have dual citizenship. My daughter, born and raised in the US and having spent no more than 40 days in Mexico over 35 years is a dual citizen of both Mexico and the US.
She has full rights to both citizenships. There are dual citizens who vote in both countries elections. The same is true of Israel and apparently Poland as I’ve known many who claim to be both Polish and US citizens and enjoy the benefits and privileges of both, including voting and social security.
Ted Cruz was apparently a citizen of both the US and Canada and enjoyed all the privileges and benefits of both citizenships ... until he decided to run for president and renounced his Canadian citizenship ... a little to late in that renouncement for some FReepers.
There is no limit to the number of citizenships any individual can hold.
No country has the right to ask any of its citizens whether thay are a citizen of another nation.This is because citizenship is decided within the country where one has it, not outside of it by any other jurisdiction.
Passports are the property of the nation who issues them and cannot be seized or demanded by any other country unless a crime has been committed by an individual, and even then a judge must order the seizure or its void.
Now if you know these things you can travel freely between countries where you have citizenship, entering them as a matter of right rather than as a matter of guest privilege, The customs examinations are conducted very differently for returning citizens, usually much more efficient and speedy.Many people do just that.There is nothing illegal about it.