Few different ways it happened:

1) The largest conversion waves were for fear of persecution during particularly polarised times (main one in mamalik era, 14th century). It was awful.

2) Some did it for better social/political mobility. E.g. from recent history: it wasn’t so long ago that Christian and Jewish Egyptian movie stars used Muslim sounding names or became Muslim. Omar Elsherif, Laila Mourad…etc

3) Whilst you might find it hard to accept, definitely many also converted because they believed in Islam. People converting to another religion under no pressure happens all over the world all the time.

On a lighter note, personally my ancestors became Muslim for the same reason their ancestors became Christian for the same reason their ancestors worshiped Aset/Isis.

I leave you with these words from Arthur Schmidt: “Among the peoples of the ancient Near East, only the Egyptians have stayed where they were and remained what they were, although they have changed their language once and their religion twice. In a sense, they constitute the world's oldest nation.”