Clint was required to kill a rattler by the script ... not because it was upsetting anyone.

As to Liz Taylor, no one seems to know for sure why she dropped out of the running to play Sister Sara ... I've never heard that it was because she didn't want to work with Clint, though. She met him when he was working with her then-husband Richard Burton on
Where Eagles Dare, and as far as I know they got along fine. In fact, Don Siegel said Taylor gave Eastwood the script in the first place because she wanted him to co-star with her. (
A Siegel Film, p. 322.)
Siegel also says that Taylor dropped out because she wanted the picture to be shot in Spain, where Burton was going to be working at the time, and the studio refused.
KC