There's a "2 foot" rule for separation, but I have seen take-offs on direct opposite sides of the main trunk, I have seen them right above the furnace, and I have seen two side by side for the same 16in joist space.
Nominally throughout the trunk there is air pressure and air velocity. At any branch-off the pressure drops and the velocity increases because air can move more easily: some of it "escapes" down the branch duct. Take offs tap-off the air predominantly based on air pressure, they don't "scoop" the air. Take-offs are slightly angled to take advantage of the velocity, and they are not exclusively pressure based.
At some distance further down the trunk (the rule of thumb is 2 feet) the velocity drops to nominal and the pressure rises to nominal. That's where the next branch-off can be.
If two take-offs are too close to each other, the pressure for both is low and both cannot tap off as effectively.
If you do it the "wrong" way it just means you have lower pressure entering into the two branches, and their velocity or flow is less than if they were properly spaced. A few of these cases won't break things, and usually you can re-balance the flow with proper throttling at the register.