TL;DR: you should probably play it the standard way, not the way you're playing it, because it promotes a poor left hand position. You should never have a higher finger coming in "under" a lower finger.
(all this advice would apply to playing a D chord on a guitar too, since they're the same fingering,
0 2 3 2. (on a guitar,
x x 0 2 3 2) )
I would say that, while there is no solid reason you absolutely have to play any chord with any specific fingering, with a good left hand position some fingerings stand out as better than others.
Firstly, for "comfortable" chords (not "spider" chords that require you to stretch out in both directions) your fingers should naturally fall tilted towards the fretboard (with your knuckle pointed towards the headstock), or at the very most 90 degrees, but never the other way.
this is a guitar but applies equally to uke. If you were to tilt your fingers the other way, you would have to over-rotate your left hand counter clockwise, and your G fingering forces this. In your picture you can see that in one position, only the right side of your left hand is touching the neck, rather than the left. This implies an unnatural wrist rotation. If you play with the uke headstock significantly raised it might not be as obviously uncomfortable as with it lower, but the problem, while reduced, will be still present.
This will effect your ability to quickly change between chords, as you will have change your entire left hand position to play a G chord (coming from, say an E minor chord
0 4 3 2)
You want to choose a position where your fingers are the most free and flexible possible, as this will aid you in changing to and from chords (and later on in adding ornaments to chords and passing notes between chords).
One last thing, you might find cutting your nails allows you to adopt a more natural left hand position, with your fingers pointing more into the neck.
More general tips for a beginner ukelelist wrapping their hands around chords for the first time: try fingering a chord, taking your hand off the neck (even shaking it around a little), then fingering it again, not one string at a time but all strings simultaneously. This will give you a) a good clue as to what hand positions feel more natural as this will be more difficult with contorted left hand positions and b) is a good exercise to help with learning quick changes between chords. Fingering chords by putting down each finger string by string is a habit you should try your best get out of immediately after learning a new chord, you want to try and build a muscle memory of the overall shape by putting down all fingers simultaneously.