You have added two Views to the same page—which is okay—that have the same filters for a custom taxonomy—not okay.
The problem is that the filters work by adding a URL parameter, and when the page is updated both Views see the same URL parameter and update accordingly.
The solution is straightforward, though.
Both Views currently have the default URL parameter added by the View when you inserted the filter. But you can change the name of the parameter on one of your Views so that they do not clash.
You need to change the name of the parameter in both the Filter Editor and the Query Filter sections. See my screenshot—where I have removed all other parts of the editor—where you need to change "wpv-analysis-category-1" to some other name that will be different than the other View.
I have another question from you in my queue about what I think is the same issue. Can you close that and, if you have problems, follow-up here?
The markup for the checkbox and its label are generated by Views and it's not possible to change this without touching the plugin code.
An alternative workaround would be to use a little JavaScript to modify the form.
Take a look at the screenshot for a local test site of mine using an "exclude-hotel" checkbox field.
Note the for attribute of the label points to the id of the input ("wpv_control_checkbox_wpcf-exclude-hotel" in my example). The problem is that both Views have an input with the same id. You need to change the id of the input on the second View and change the for attribute of its label to something unique, and then the filters of the two forms will work independently.
Are you able to do that?
Why not close the other ticket and continue here with the related issue (I'm not sure what the problem in the other ticket is).