If a journal is not indexed this way, is it an academically honorable one?
If we momentarily disregard from discussions regarding the cons of ISI and Thomson-Reuters who run the service etc. and focus on the usefulness of ISI indexed journals for ones career, the answer is yes, it is important at least to some extent. The importance is in part depending on your discipline since ISI indexing is not evenly distributed over disciplines. But generally speaking the ISI listing means the journal publishes papers that are referenced, which is an indication that it is research of some quality and importance.
This does not mean non-ISI-listed journals are not "honourable". But, when choosing a journal in which to publish, you need to make sure it is read by other in your field so that your research is seen and your ideas known by others. You should make a survey of journals that are of reference and if you find ISI-listed journals there is a reason to consider them if your papers fulfill their quality criteria because they will be seen as prestigeous references when you are evaluated for a position etc.
I don't think "honourable" is the correct framework to think about. My general understanding is that most reputable journals will be ISI indexed, and so if you are considering publishing in a journal which is not, you should look hard at whether it is legitimate, and whether people in your field will respect publications in it. You should look at the same thing for ISI-indexed journals. There are many journals which are ISI-indexed, and I have no reason to believe are not run legitimately, which I have never heard of, and which I would never recommend to someone I know as a place to publish (I don't want to pick on any particular one, but if you go to Web of Science and search for the name of your field, you will find plenty of them). An article in a journal I have never heard of makes a very poor impression to me on a CV, so it is worth researching more carefully what the "word of mouth" reputation of journals is in your field.