There is no general answer (i.e. an answer that would be based on the meanings of words as defined in general-purpose dictionaries) that can be given to this question, apart from the obvious non-honorary, suggested by @user140086. If there is a word that can be used to denote all members of a particular organisation other than the honorary ones, it has to be a word that is explicitly defined in the bylaws of that organisation to have that precise meaning.
Using the word real for that purpose would have the implication that the honorary members are not really members of the organisation, which would make one wonder what was the point of admitting them as such. (This has already been observed in a comment by Kris.) Indeed, the honorary members could be insulted by the implication that they are not real members. While it may perhaps be understandable that the non-honorary members may sometimes be tempted to use real in this way when speaking informally, among themselves, its is not something that should ever appear in the organisation's formal communications. (It is not crucial to answering this question, but it should be noted, incidentally, that the differences between the honorary and other members vary greatly from organisation to organisation: at some places the honorary membership is largely nominal, but at others the honorary members may be involved in the actual activities of the organisation.)
The terms regular and ordinary, proposed elsewhere on this page, can mean the same as non-honorary if they are so defined in the bylaws of the organisation, but they cannot be assumed to have that precise meaning in the absence of such an organisation-specific, explicit definition. This is because different organisations have different classifications of members, and in some of them regular or ordinary may be used in contrast to, say, associate, temporary, senior, or emeritus, rather than in contrast to honorary.
So the only answer that can be given to this question is: look up the bylaws of the relevant organisation and use whatever term is defined there to have this meaning. If no such term can be found, then the only term that can reliably carry this precise meaning is non-honorary.