'Star-crossed lovers' are two people who, although in love, have natal charts which are 'crossed'. 'Star-crossed' is, effectively, a technical term in astrology indicating that there are aspects of the charts of the two lovers which, when compared, show that the forces of fate will tear them apart or, at least, prevent them from being happy together.
In detail there will be aspects of the planets (wandering stars) and other parts of the charts which have powerful ninety degree angles between them (a ninety degree angle is a 'square aspect' in astrology and is usually considered to be an indicator of negative forces operating on the subject of the chart. Four planets with square aspects to each other can form a "Grand Cross" which is considered to be a very negative element of a chart). A true believer in astrology would, of course, say that there are also aspects of the combined charts which led them to fall in love in the first place.
You don't have to believe in astrology, and certainly not in the fixed fate interpretation of it, to consider that Renaissance people would have taken the term literally. From our perspective it is metaphorical but from Shakespeare's perspective it was not.
If we write "star-crossed lovers" in most contexts in the 21st century then the phrase is metaphorical in the same way that calling someone 'phlegmatic' is metaphorical, but in the late 16th and early 17th centuries when Shakespeare was writing all educated people accepted the validity of astrology and the existence of the 'four humours of the body' so 'star-crossed' and 'phlegmatic' were literal uses of technical terms for them.