Though not opposites, they would certainly contradict each other.
Maybe in certain methodology, but mostly as a side effect. They can't co-exist within the same human, but they can co-exist easily in a social group. Neither actually has much of an impact on the other. Both are internally trans-formative processes and in that way they are completely the same. =)
This is generally my primary challenge to Abrahamic-based religions. If you cannot effect someones internal spiritual process why do you waste your time actually trying? =) Whether it is RHP or LHP it is personal -- between you and your own inner machinations. What could any priest or prophet do for you? Alas, nothing... nothing at all.. No redeemer nor god can thus save.
Now, that being said in certain orders of faiths there are monks and whatnot whom do work on the proper RHP processes personally -- but, the lay members of the faith have nearly no participation in this nor do the people whom play priest at mass. These orders of monks actually do something on their own behalf to achieve spiritual awareness, and probably know something of it. Though, undoubtedly they are knowing that they must do something not rely on prayer to achieve it. This is the purpose of vows and things. They deny the personality and quiet it aiming toward spiritual knowledge. If you ever see a rich holy man immediately doubt his credentials -- he's missing the point. =) The RHP process cannot work without an active denial of the things that taunt the personality.
There would be no need for this RHP person to to "at war with" the LHP-type. Again, anyone truly knowledgeable knows both paths lead to the same wisdom. It is merely a matter of personal nature which differentiates. The goal of each is completely the same in the truest sense. They _barely_ even conflict past the base operation notion. The RHP person doesn't even view the humanness as bad, but merely an obstacle which interferes with the processing of the information.
It is similar to comparing an aleopathic doctor (M.D.) to a doctor of osteopathic medicine (D.O). They're both doctors who study medicine and heal people, but use different methods... silly business to say one method is better or worse than another. They are different and both work. =)
Wise persons on either path (of which there are so few) can aptly point this out and recommend a course which suits the questioner not themselves. =)