The following should do what you’re after:
/root/user[login='user1' and
name="User 1" and
profile="admin" and
profile="operator"]
Having two tests for the profile value might seem odd, but as there are multiple profile nodes then the condition will be satisfied as long as at least one node matches the test.
The reason you can compare profile directly to a string, even though it actually is a node is that the string-value of an element node is the string-value of all its descendants concatenated together, which in this case is just the contents of value.
If profile contained more elements than value you’d have to use a slightly more complex predicate test to determine the existence of a matching profile node based just on the value (this should work with your updated question):
/root/user[login='user1' and
name="User 1" and
profile[value="admin"] and
profile[value="operator"]]