I did that very same thing. Right for everything except bow and I shoot pistol right handed but use my left eye like you do.
For new equipment, no big deal. I bought a used bow, so the selection was far less but I found what I wanted at a good price.
The rest was just practice and reps. One off season and I was shooting better than righty.
One good thing is that if you use a wrist release, it is much more convenient hunting where I put it on when I wake up and take it off at sunset. Being right handed, it's not a big deal to have it dangling on my non-dominant hand all day.
The other good thing is that my left hand isn't mentally associated with pulling a trigger so I feel I have far less problems with trigger slap or any of the potential issues with using your dominant hand. This could be 100% mental, but I think it's real and I've never had any trigger pull issues knock on wood.
I can't think of many negatives except a minor one where your bow is in your right hand so I also use my rangefinder on my left. It still gets a bit awkard but nowhere near enough to come close to the benefits.
Being able to see is 1500X more beneficial than using your correct hand in my opinion.
