Student or Learner
I took an umbrella with me for fear that it would rain. (I wouldn't use "should" there. Perhaps that is an AE/BE difference.)
1. ...for fear that it would rain.
2. ...for fear that it should rain.
Do BrE speakers prefer #2 to #1? Is #2 unacceptable in U.S. English?
The whole thing sounds a little old-fashioned to me whatever modal you choose.
I'd probably me more likely to say, "in case it rained"