A. wants the company to pursue a more aggressive cost-reduction strategy because it fears that low-cost competition from Asia has the potential to put the company out of business
"a majority" needs plural verb. SVA error
B. wants the company to pursue a more aggressive cost-reduction strategy because they fear that low-cost competition from Asia has the potential to put them out of business
same as A.
C. fear that low-cost competition from Asia has the potential to put the company out of business and want the company to pursue a more aggressive cost-reduction strategy
seems fine
D. want the company to pursue a more aggressive cost-reduction strategy because they fear that low-cost competition from Asia has the potential to put them out of business
"they" refers back to A majority of the shareholders ,but "them" is too far to refer back to the same subject. still hold on
E. want the company to pursue a more aggressive cost-reduction strategy because they fear that low-cost competition from Asia has the potential to put it out of business
"it" is ambiguous.
Between C and D, C conveys the meaning more clearly.
IMO C