Hi there
Raja is on vacation currently, so I've taken a look at this.
Reading through this, it seems like the question does relate to the conditional display group option in forms (which uses JS to conditionally display content according to changes in selections in field inputs in the form) rather than the wpv-conditional shortcode which is evaluated on the server and is unaffected by subsequent changes to form inputs on the front-end.
It is certainly not clear, but when using a taxonomy for such a condition, the condition must be entered manually, and the value you compare against depends on whether the taxonomy input is displayed as checkboxes or a select dropdown.
If checkboxes, then you should compare against the term name (not slug).
Here's a simple example I verified works on my own test site:
[cred_show_group if="$(colour) eq 'Red'" mode="fade-slide"]<p>The colour is Red</p>[/cred_show_group]
If the taxonomy is displayed as a select then you need to compare with the term id (i.e. a number).
It's confusing, we have an internal ticket to improve this, and I've added your thread to that internal ticket to help bump its priority.
Meanwhile, I visited your site and checked the form. I guess you've done some work on it, as I couldn't find a conditional group for exhibitor-type.
But I did notice a JS error on the page, and as conditional groups work via JS, this will need fixing or they cannot be expected to work.
I looked through the markup of the form, which has been extensively manually edited. I copied it into a code editor to help formatting, and I noticed a problem with the following markup:
<div class="col-md-6">
<div class="form-group">
[cred_show_group if="( $(page-header-option) eq '1' )" mode="fade-slide"]
<label>Looping Video File - Please choose or upload a video in .mp4 or .mov format, and with a
100MB max size. Also, please no sound or word overlays. <span style="color:red;">We
recommend a length between 7 to 30 seconds.</span></label>
[cred_field field='header-video-file' force_type='field' output='bootstrap']
[/cred_show_group]
[cred_show_group if="( $(page-header-option) eq '2' )" mode="fade-slide"]
<div class="form-group">
<label>Still Shot - Please choose or upload an image that is at least
1900px wide by 850px tall. Only .png, .gif and .jpeg formats supported. No words or
logos on this image please.</label>
[cred_field field='hero-image' force_type='field' output='bootstrap' previewsize='thumbnail']
</div>
</div>
[/cred_show_group]
</div>
It's important to realise that whatever occurs inside cred_show_group shortcodes may be excluded in their entirety. The opening and closing divs and opening and closing cred_show_group shortcodes are messed up: if you deleted both cred_show_group blocks the remaining markup would be broken.
So I would first perform a careful inspection of your form to identify such potential problems and fix them.
Then try again with the conditional group that you were having problems with based upon the above directions.