Like dun said, since Balancers are a blend of registered Gelbvieh and Angus (red or black) they are no more prone to pinkeye than any of the parent breeds.
Balancers can be between 25% and 75% Gelbvieh and the balance being Angus. Most people assume that Balancers are 50% Gelbvieh/50% Angus. So, you need to ask what the percentages are when purchasing Balancers.
If your current herd has a large percentage of Continental blood (Charolais, Simmental, Limousin,...) you likely want a Balancer that has at least 50% Angus. If your herd is primarily British breeding (Angus, Shorthorn, Hereford, S. Devon) you will probably want 50%+ Gelbvieh.
Now, with all that being said, if your cattle are sold on a grid that rewards marbling, you need to continue with a higher percentage of Angus. If your cattle typically go into grids that reward you for improved yield, you probably want to use a higher percentage of Gelbvieh.