MikiBg
I think you need to qualify the definition of isolation for the motor and drive.
It is common practice to isolate the motor for maintenance reasons (and usually lock off the isolator). This would not typically be a contactor, but a manual switch/isolator. It is typically positioned between the VFD and the motor but the expected practice is to power off the VFD before opening the circuit to the motor. This often happens with pumps and fans alike.
There are drive companies who say it is ok to switch on the output but this is not the same as saying is is good practice. It isn't. If you open a circuit between a drive and motor when it is running, then this is quite bad practice and depending on the design of the VFD, it will either stop and alarm (the VFD will 'see' a very high impedance) or go bang.It may keep running but this is also not good. The reason is, if the isolator is then closed into the output of the VFD the motor will demand a very high current (it is the same as DOL) and likely trip the VFD, at best.
So, isolating the motor is common practice when providing maintenance on the motor/load and is usual the isolator is visible to the person working on the load.
A contactor on the output, unless integrated into a drive bypass system with mechancial interlocks and logic to prevent incorrect opening/closing of the supply, is unusual and probably not recommended.
Addressing your specific comments:
1. With line contactor (upstream of VFD). Some say that it's good for VFD to be disconnected from power supply if it is out of operation for long time (e.g. standby pump unit)
As already mentioned, if you are leaving the VFD without power for >12 months or so, it means the caps will possibly need gentle persuasion to function properly and the occasional power-up is often beneficial. This would be the only reason you would need consider not bringing a VFD back on supply without any thought about how long it has been out of action. Otherwise, it's good to keep power on the drive and then you can at least see the keypad in case any specific errors are visible
2. With load contactor (downstream of VFD). Some say that it's better to isolate motor from VFD when it's not running
I think you need to understand from the 'some people' what they mean by "better". Better for what?