I'm from Northern Ireland - birthplace and home to the vast majority of Orange Order Lodges and members.
It is a relatively secret organisation, and has certain traits similar to the Masons, but in my opinion it does not appear to be as syncretistic and mystical as them. It is practically only for orthodox Protestants, and professes to uphold and protect the Reformed Faith. I believe this is laughable given that the vast majority of members in my opinion are not even true believers, wouldn't know the Reformed Theology from Hinduism and are more interested in a pint of beer than a catechism, most are cultural Protestants at best.
There are true believers in it, there are a good number of ministers in it.
My biggest issue with it from a Christian point of view is that I would find it very difficult to square up how I could speak to a Roman Catholic about Christ one day and then be seen by them and perceived by them the next as being in a organisation that 'hates' them.
Here is a extract from the Reformed Presbyterian Church of Ireland's Testimony
"There are several secret societies in existence. Some are older than others and some are more prominent than others. The Church's attitude to such organisations must be determined by a study of Scripture. From such a study we find that the teaching and practice of secret societies are in conflict with the Word of God in the following ways:-
1. Unscriptural Secrecy
The practice of secrecy is contrary to the teaching of the Word of God, and to the example of the Lord Jesus Christ. He said "I have spoken openly to the world, ... I said nothing in secret." Secrecy is also damaging to society and is contrary to its well-being. "Whoever lives by the truth comes into the light, so that it may be seen plainly that what he has done has been done through God."
2. Unlawful Oaths
Membership in secret societies involves taking an oath before being aware of the obligation. No man is at liberty to bind his conscience by oath without a knowledge of the nature and extent of his undertaking. In doing so he is being bound to a law other than, and, in the light of further knowledge, possibly in conflict with, the revealed law of God. "There is only one Lawgiver and Judge", "It is a trap for man to dedicate something rashly and only later to consider his vows".
3. Unsocial Benevolence
The benevolence of secret societies is confined to a "brotherhood" which is not warranted by the Word of God. Scripture gives clear direction for our good works. "Therefore, as we have opportunity, let us do good to all people, especially to those who belong to the family of believers."
4. Unchristian Fellowship
True fellowship exists only between those who are united by saving faith to the Lord Jesus Christ. Freemasonry, for example, excludes the mediation of Christ and accepts, as brothers, representatives of many non-Christian religions. Scripture, however, clearly teaches that we can have fellowship with one another only because "our fellowship is with the Father and with His Son, Jesus Christ.""
Then specifically concerning the Orange Order,
"The Orange Order recognises the need for a faithful witness against the errors of Roman Catholicism and that all true Protestants should be united in their faith. Nonetheless, the first three reasons mentioned above (Unscriptural secrecy, unlawful oaths, unsocial benevolence) can be cited against membership in the Orange Order. In addition, we believe that the Orange Order is in error because:-
(a) it usurps the place of the Church
God has ordained the Church as His instrument in the world for the defence of the Faith and the propagation of the Gospel. Scripture teaches that "the Church of the Living God" is the "pillar and foundation of the truth." The existence of a secret society which claims to have this authority of Christ, the Church's King and Head;
(b) of its political emphasis
The Orange Order lays great stress on the political aspect of the Revolution Settlement of 1688. By doing so it fails to acknowledge the Kingship of Christ over the nation. It was precisely because the Revolution Settlement did not acknowledge either Christ's Kingship or the doctrines of the Second Reformation that Covenanters stood aside from it;
(c) of its unqualified allegiance to the British Constitution
In becoming a member of the Order a person commits himself to support and maintain the British Constitution and the Laws of the Nation. Such allegiance denies the Crown rights of King Jesus whose kingly rule is not acknowledged by this Constitution and whose authority is flouted by unbiblical laws.
For these reasons it is inconsistent for Christians to identify with this Order.
The Reformed Presbyterian Church believes that the Christian should not become a member of an oath-bound secret society. It strongly affirms that Christians are called to show benevolence to all men (Gal.6:10), to enjoy true fellowship (1John 1:3), and to bear a faithful witness in the world (Acts 1:8). This must be done in a way which God has directed and which will honour His Son, Jesus Christ."
Source:
The Church and Secret Societies