Yes, you are correct...it is a custom that
wasn't always accepted by all observant Jews. In the early part of the
20th Century, Orthodox German Jews did not all always keep their heads
covered. Most did, but not all.
However, that being said,
when a custom becomes as widely accepted as covering one's head at all times
that it becomes a "tradition", it also usually is accepted as a "law". I
fluctuate between wearing a kipa and not, depending of where I am going.
If the community is less aware of Jewish traditions, I might wear a cap or a
funky hat or, even, nothing at all....what is paramount is always being aware
that there is something above us at all times.