Why is 持 in the sentence 这些持反对意见的员工表示，……?
持, here, is shortened form of 持有.
持 has a definition on MDBG that reads:

to hold

持有 is defined on MDBG as:

to hold (passport, views etc)

You, correctly, translated it as with, which also works here.

Another term that might help you wrap your mind around this term and usage is the word:
持方
CedPane defines it as:

side (in debate)