Minimal splitting is accepted as long as the fruit remain sweet and edible ,till ripe and can be used for fig preserves.
List:
_Col De Dame,White and grey,possible Black,will know when it ripe.
_JH Adriatic
 _Kadota (It has other problems ,with proper ripening in my climate,but is souring resistant)
_Nero 600M also called ,Valle Calda
_Ischia Black
 _Battaglia
_Nebo,From Nelson,in Canada
Edit Note:
St Anthony,(Italian Honey),is one of the best in rainy climate and I miss to write it down.
May be ,Because I personally do not find the flavor enough superior for my wants.
Of course whatever did not sour in my climate could sour in other climates worse than mine,because they can take so much till a point.!
Please post your finding,of other cultivars, or contradict me.?

Some of the good performers here during our two weeks humid and wet period:
Celeste jr
Blue Celeste
Sal's
Dark portuguese
Hmari
Rmali,

There are others that ripened before or after the wet two weeks that we had. 

Herman, I lost 90 percent or more of my crop this season once the rains started and wouldn't stop. The only fig that did not split or sour was the O'Rourke. It even retained most of it flavor and wasn't watery. The rain wouldn't stop this season, it started with 13 days of rain out of 15 days and it didn't stop there. We had days of 3" and more. I had a 4 day total of 11 inches at one time. So for now I'd have to give the O'Rourke the 2 thumbs up.
"gene"

Gene:Good to know,and very important to accentuate ,O'Rourke as a rain resistant cultivar.
I do not have it,but have information from another gardener in the south,that it is a fact ,your conclusion.
This is the information my post is trying to find out.
Thanks again Gene.
PS:The fig I started my list with,are not early figs,and they did not ripe in this Summer conditions,but I know they are resistant to rain from last year 2011 season,which was just as bad,with 22 inches of rain in August and 70 inches of rain for the year.
The  cultivars that did ripe the first fruits this year and they were just fine is JH Adriatic,and Nebo, at this point in Time.

O'Rourke has done well in NH during wet weather.
Had a couple today that we let fully ripen and we rated it 9 out of 10.

This year with all the rain we had and the watering done I think anything that would split must have.
What did not split;
LSU Purple - were excellent
Celeste - excellent - 7 years old - never dropped any figs
Alma - excellent
Ischia Green - excellent
Gino's - good
Texas Everbearing - excellent
Scott's Black - excellent
Brown Turkey - good
Mary Lane Seedless -excellent first year with any figs (7 years old)
Conadria - too watery - usually my favorite - not this year
Hardy Chicago - not very sweet, watery - not a good year

What did split;
White Paradisio (from Morle) - watery, but sweet - not a good year
St. Jerome, split almost in half but were sweet - not a good year
Blanche de deux Saisons -split but were excellent -no comparison -new

I don't know why I had no souring. Perhaps it's because the figs that split I picked earlier then I would have had they not split )hmm that's sounds too obvious).