As lawyers know, the word "and" can be quite significant. We tend to be sensitive to its use. It's conjunctive. So if, for example, a legal right or duty is conditioned on the existence of "X and Y", then normally both X and Y must exist in order for the legal right or duty to apply. On the other hand, if it's conditioned on "X or Y" then the right or duty will apply if either X or Y exists.
When one pledges loyalty to a "Jewish and democratic state" then, one is in the legal sense pledging loyalty to one that is both Jewish and democratic, not one or the other. This fact seems to create difficulties.
The proponents of the oath maintain that Israel has been a Jewish state since its foundation; it was, after all, created to be a homeland for Jewish people. This is apparently noted in its Declaration of Independence (from what, I wonder?--I must check that out). The fact that it may be a state associated with a particular religion would not in itself make it remarkable. There are nations which contend they are Islamic, as we know. As loyalty oaths are fairly common, it would be unsurprising if such nations required loyalty to an Islamic state. Why should there be any outcry over the fact a Jewish state requires an oath of loyalty to itself as peculiarly Jewish?
Citizens of the U.S., used to the idea of the separation of church and state, may claim that a nation cannot be simultaneously Jewish (or Islamic, or Christian) and democratic--although some of the louder and more belligerent among them seem to claim it is itself a Christian nation. But that separation is one dreamed up (fortunately, I think) by the shrewd lawyers, merchants and farmers we call the Founders; it isn't a universal characteristic of a democratic government or nation.
But Israel is in this case, and in others, extraordinary. Some of its population isn't Jewish, and apparently don't wish to be. It's unlikely they will be eager to pledge their loyalty to a Jewish state of any kind. It is surrounded by nations which are not Jewish, and apparently don't wish to be, and indeed would rather there would not be a Jewish nation next door to them, or perhaps anywhere in the world. So, requiring such an oath in these circumstances appears unwise, as a purely practical, political and military matter, because it is bound to create difficulties among Israel's population, its neighbors and, because of the importance of the region, to the world at large.
This kind of problem will arise whenever nations are considered as anything but secular entities. When they are not merely nations or governments, but are instead nations, governments and religious, or ethnic, and exclusively so, difficulties result, due to intolerance and discrimination.
So we should be thankful to the Founders here in this great republic, and hope that their work won't be overturned by those politicians, pundits and preachers of our time who seek to do so.