I have not seen any requirement along these lines.  Not really comparable to right hand vs left hand.

There is no different average whether you throw with a thumb, or two handed.  If you throw the ball with your right hand, or throw with two hands on your right side, the right hand is your dominant hand and the USBC recognizes both as right handed.  The only issue you would have would be related to equipment.  Assuming when you bowl two handed, you do not use a thumb, you would not be able to use the equipment you use when you bowl with a thumb due to the USBC's equipment specifications on weight holes.  All holes must be used for gripping purposes.  If your thumb hole is unoccupied, it is considered a weight hole and therefore illegal. 

Kinda of a different question than the topic poses, but this got me thinking.

Will USBC get to the point of allowing a solid slug(like an IT or Switch-Grip) to fill the hole to be used when using two hands? It would be the same as not having a hole.

One would probably have to do some research on the drilling to make it effective for both styles, but it should be doable.

That.... is a very good question. But I'll ask another question: as the IT or Switch-Grup already exists, what is to stop a bowler from having the PSO drill up the ball, but not drill up the slug, and leave it able to be put in and taken out now? I mean, technically there is nothing in the certification process to show that to be illegal..

If the drill for the slug is done according to the drilling specifications, but no hole drilled in the slug, would the slug and the still be legal, especially for two-handed use? a good argument for it would be that a bowler wants to use the same ball to shoot at spares and uses fingers and thumb (read: Osku), or wants to switch between one and two hands without having to switch balls.

BL.

I'm not an IT or Switch Grip user, so there may be a way to do this that I'm not aware of. But how would one remove a solid slug when wanting to use the thumb hole? From what I've seen, you need to be able to put your thumb or one of those rubber tools in the hole to be able to twist the slug out.

I'm glad you asked that because not being a user of a removeable thumb slug, I was wondering that same thing.

Removing it would be simple. If you made a slot in the top of the slug that a nickel or quarter edge could fit into it would just twist out with ease

Bro, I gotta say that you've really opened a can of worms here! 

Okay.. there's nothing listed in the USBC for what you're asking, and as it is only the USA's governing body, I went further up to the IBF, which governs everything worldwide, and they only break things down by division and country...

.. so what the hell, eh? I looked up Australia's governing body, to find their certification rules.... and nothing.

Looked at the UK's... nothing. Ireland? nothing. Canada has this:

What if a bowler does not use their thumb for a strike ball but does use their thumb for
a spare shot?
As of August 1, 2020, a bowler who doesn’t use the thumb during a delivery cannot have a thumb hole or a balance hole. If the ball does, it is illegal and games are subject to forfeiture. All holes drilled must be used for gripping purposes on every delivery.

Big grey area here. Obviously, a 2-handed bowler can't have a thumb hole, but is a hole drilled for the insertion of an IT or switch-grip considered a hole, even if the IT/switch-grip isn't drilled for a thumb?

I'm not even going to try translating the Korean or Japanese federation, so I see where it can be legal, but I can also see that because it isn't illegal doesn't mean that it is legal. It's neither legal, nor illegal.

BL.

Chapter 8 Equipment Specifications

5. Ball Plugs, Inserts and Slugs.
a. Removable devices must be approved and on the Approved Removable Bowling Ball Devices list.
b. Ball plug or slugs may be used for the purpose of re-drilling a ball. When a slug is used, there must be a hole drilled
completely through the slug leaving no void at the base.
c. Plugs, inserts, tape and slugs may not extend beyond the surface of the ball.

It is my understanding that a solid switchgrip would be deemed illegal due to there being a void at the base of the grip, ie where the grip locks in.

An internal void anywhere on the ball is deemed illegal.

I feel it should be allowed but when we debated this a few years ago that was the reason we came up with for it falling outside the rules.

+1