There’s much more to oil than the viscosity, which is what the 5w30 means.
In your handbook it will say that the oil needs a certain manufacturer specification – and they all have their own. My Passat for example needs 505.00 or 507.00. These are VW specific numbers. Ford have their own numbers.
Some engine oils meet multiple specifications from different manufacturers, but it does tell you on the back of the bottle.
You may not think it’s important, but in the case of my Passat, it’s a PD engine (as many pre 2008 VAG cars are) which means the injectors are driven off the camshaft individually. This means that the cam lobes for the valves are half the width, and subject to more wear than normal. The VW oil spec for PD engines gives enough lubricity to cope with this extra pressure.
So it is important – much more so than the brand.