Physical seasons, and the modern western calendar, are both based on the sun. Having two moons wouldn’t make a difference there.
Two moons would make the ocean tides more complicated, though.
Perhaps we’d have entirely solar-based calendars with four month-like divisions for the seasons, based on the angle of shadows cast by the Sun (I hear the Mayans had these huge dial things that just counted from 1 to 365) and leap days added onto one season every few years.
Seasons could still probably be broken down further than that. A system of 8 solar months would make sense. Basically the times of lots of change in day length vs stable day length.
Also so long as one of the moons continued to roughly correlate to menstrual cycles it would probably have some cultures tell time by it
Many indigenous peoples tell the time of year by the stars rather than the moon. A certain constellation just became visible? Must be X time of year!
Given our propensity to watch the stars and moon, I think we’d figure out some month schedule if we wanted one.
Months really don’t matter all that much because the seasons are still based the Sun and the planets tilt. The days get shorter and longer each day and that’s pretty easy to observe.
(We might actually get a month that makes more sense if we throw out lunar cycles. One that aligns with the week.)
Earth’s moon is notably big. Relative to the size of its parent planet, it’s easily the biggest* in the solar system (or second biggest if you Stan Pluto as a planet). If there was a second moon, it would likely be a lot smaller. So, I don’t think it would have much practical effect on things like tides or timekeeping. It would still have cultural significance in things like mythology and astrology. If we could observe moon-moon interactions we might have discovered gravity earlier.
/* in absolute size, there are a couple of larger moons, but they’re moons of giant planets so Luna still wins in relative size.
@Epicurus0319 solstice and equinox my dude.