On my NH TC-30 hydro, one should always come to a full stop and use the clutch when changing ranges.
Having said that, I can often change without using the clutch, but am stopped or very nearly so and never under load when changing range. Most of the time, you select a range for a task and stay in that range, so this is not a frequent action.
There are probably some hydro trannys that do not use a clutch and that may even allow range shifting 'on the fly'.... the dealer can tell you if it applies to their model.
If you are new to hydro tractor transmissions, keep in mind that when you press either the forward or reverse pedal you are initially in maximum (for that range) torque/minimum speed mode and as you press the pedal more you are going toward the maximum speed/minimum torque end of the curve.
The power available is dependent upon the throttle setting and generally should be at or near rated power RPM (the RPM required for rated PTO speed of 540 RPM) in order for the charge pump to keep up with the maximum demands of the variable displacement (main 'traction') pump.
If you approach an uphill and the tractor slows, easing up on the pedal is more likely to keep you going than pressing down more. Depending on steepness and load, you then may have to stop and select a lower range.
The hydro pedal(s) do not act like an accelerator. You get used to it quickly when you understand what it is doing.
Rip