I am not a beer drinker at all. My choice is white wine. Does anyone have any insight as to the white wines I will find in Ireland. I'm assuming the better restaurants will have a good selection, but what about the average pub?

The average pub will have plonk, I would say. Depending where you are in Ireland, you may be able to find a wine bar, but they don't have the same atmosphere.

When in pubs, you might try cider.

Wine is increasingly popular in bars - many have good selections.
The pallet for white would be New World, French (like Macon and Chard) or Italian White. I would have to said that the smaller the towns - the weaker the selection!

In most pubs I wouldn't drink white wine - but settle for one of the many other choices (I don't drink ale either - and 1 beer only with certain ethnic foods - in places where local lager is the standard - Germany or Czech republic).)

The most common wine option in pubs is a small 18.5cl bottle (just over a quarter of a standard bottle, a measure sometimes referred to as a "snipe"). Typically, the number of options is about 4 white and 4 red, but it can be as low as one of each or as high as about six. New world wines dominate. Generally you get nothing memorable, nor anything too offensive.

Drink Irish Whiskey, forget the wine

Must concur with previous opinions.
Due to some reason, probably one of convenience, the white wine options in pubs are, in the main, confined to fairly nasty offerings in screw top quarter bottles - typically sharp acidic Chilean Sauvignon Blanc or "fruity" Chardonnay from Australia or South Africa.
Your palate (and liver) deserves better.
On the bright side, you should fare much better in restaurants - although prepare to pay, as most places show little mercy when it comes to mark-up.