David's father believes them platonic, everything that is manly and safe. He has been known to pat Jonathan on the shoulder in a fatherly way, because he does not think the King a good father (though, naturally, the King is a good man; he is the King, after all). His kindness (his blindness) has moved David to tears on more than one occasion.
Michal believes them romantic - and, because she would like some part of David's love to be hers alone, otherwise chaste. Her unhappiness is the only thing that breaks Jonathan's heart; she is his beloved baby sister and he would rather die than hurt her. He may yet. Loving David is dangerous, he tells her, but it has never stopped either of them.
Saul knows them to be lovers - this humiliation is something Jonathan will never forget - but he steams in silence and does not denounce them in public. He would not have the court - or anyone - know that David has seduced his son and heir into compliance; that the upstart David of Bethlehem is master of more than just a sling and the hearts of the Israelites.
When they are together, though, often it seems that what other people think is unimportant; that it is only worth mentioning if they are planning to do, not say. So when Jonathan is in David's arms, he forgets Michal; and when David is in Jonathan's, he forgets Jesse. Then their only troubles come from Saul, who will kill David if he finds them together again. (David fears that he will kill Jonathan, too; secretly, so does Jonathan.)
But even Saul is unimportant in that first moment, when they see each other again. Sometimes it is only a look, for David cannot speak and Jonathan dare not. But love remains, like the inevitable repetition of dawn. Jonathan cannot stop loving David, in any way people think, and David will not stop loving Jonathan.