I'm the same as you - everything single-handed I'm a leftie, still a leftie with a rifle and guitar, but hold cricket bat and golf club right-handed for reasons unknown. Agree it is an advantage if you can be truly ambidextrous, especially for river fishing, but also has its uses when boat fishing - if your partner is a right-hander, you fish left-handed, and vice verso.
I've been a leftie boat fisher all my days and the thing you will find is that lefties develop a ridiculous amount of lean out to the side, due to years and years of fishing with right-handers. There is another thread a guy started on left handed fly tying, which went off on a tangent into casting and we posted some pics of us lefties in boats on it.
Also very useful if you ever get into salmon fishing to learn to Spey cast right and left-handed. The one other thing I do right handed is hold a spinning rod, so when it came to the point where I was learning to Spey cast, I didn't know which way I wanted to hold the rod, so I learned both ways, and it is very useful being able to do it both left hand and right hand up the rod.
As already suggested, it would be a good idea to get a lesson from a pro instructor now, while you are not too set in your ways, and see if you can get into the habit of being able to cast with both hands. If you find you can't master it with both hands equally, don't worry - you will be in good company. If you can only go with one hand, go leftie. Although I am in part saying that on behalf of the left-handers union

, there will be more times you are fishing with a right-hander than a left hander*, so it is useful to be a leftie. Apart from boats, if you and a right hander fish a river it gives you an 'easier' bank each, or if you and a right-hander fish a hill loch off the bank, you can set off down one side each and both have the wind over your correct shoulder... and so on.
Col
* Having said that, I was once a member of a party of six that went on a boat fishing holiday to Chew and Blagdon, and four of us were left-handed