Hi Katie! When you say "conflicts" do you just mean bookings? GCal (and probably other calendar apps) allow you to add other people's calendars to your own. If you're all in the same google workspace, you can just search for people and it'll show their events in your calendar.
Trello might be a good option if everyone doesn't have gmail for example. You could have one master calendar board, and the cards would represent bookings/events. The idea would be to assign a due date and a member to each card, and you could then use the calendar power-up (or native calendar view if you have Trello premium) to see all items in a calendar. In terms of assigning cards to people, you'd need to add them all as members to the board. If you don't want to do this for whatever reason, another way is to create custom labels titled with each member's name and apply these labels to the relevant cards. From there, you can either view everyone's cards on the calendar or filter it to only see certain member's cards.
Hope that helps!
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