I have a bodyguard in order to protect myself
Solution 1:
As @deadrat mentioned in the comment, what you were told is nonsense. The linked is a list of stative verbs that I found on the internet. The reason to classify those verbs as a stative verb is to emphasize the fact that those verbs are not (generally or usually) used in continuous (progressive) tenses as the link shows.
I have a bodyguard in order to protect myself.
It is not grammatically incorrect. The purpose of having a bodyguard is to protect myself. It is just not as idiomatic as "I have a bodyguard to protect myself" because using in order could be considered redundant.
Let's compare the sentence with the most well-known stative verb to be:
I am on a diet (in order) to lose weight.
If what you were told is right, you can't use the above sentence as to be is a stative verb. It is not diet which is to lose weight.
Using stative verb with to infinitive which indicates purpose is fine. But some of them may not be idiomatic. It doesn't necessarily mean you can't use to infinitive with a stative verb. You have to learn how those stative verbs are used idiomatically on a case-by-case basis.
Edit: To have is not always a stative verb. The most notable case is when it is used to mean to eat or as a causative verb, it is not a stative verb.
Let's consider the following sentences:
I have never felt any need to have a bodyguard (in order to protect myself). But sine the ISIS attacks in Paris and San Bernardino, I have just decided to hire one. Now, I have a bodyguard (following me wherever I go 24/7) in order to protect myself.
I don't think to have in the above sentence is a stative verb.
Solution 2:
I'm not sure about whether your sentence is grammatical or not, but in order to is usually used to express a required condition or a purpose. You cannot fulfill a required condition by being a state. You also cannot have a purpose behind being a state.
I think your confusion has something to do with the belief that the to in an infinitive can be replaced with in order to or so as to. Sometimes the to-infinitive is used to denote the function of the object but not the purpose of doing the verb.
I have a bodyguard to protect me.
In this sentence, the to-infinitive is used to denote the function of the bodyguard. It, however, does not denote the purpose of doing have or what doing have is required for. In fact, it is impossible to do have because it is a stative verb (in this context). So, you shouldn't replace the to with in order to.
As you correctly state, in I need to study in order to pass the exam, need is a stative verb. In this context, it expresses an obligation to do the to-infinitive. In order to is commonly used with such verbs (must, have, need) to emphasize that doing a verb is necessary for accomplishing something else. The meaning of your example sentence is clear: studying is necessary to fulfill the purpose of passing the exam.
You cannot fulfill anything (a purpose or a required condition) by doing a stative verb because you cannot do a stative verb.