Thank you for sharing these details and I apologize for the delay in getting back on this.
I've performed a couple of tests on my website, with similar taxonomy filters and I couldn't reproduce this issue.
When the "Any of the following" option is selected, the taxonomy query uses the "OR" operator and not "AND", as expected.
(strictly technically speaking, "IN" operator is used in the actual query)
Here is a screenshot of the taxonomy filters from my test website:
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And here is a screenshot of the results shown on the front-end:
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This suggests that something specific to your website is involved, and it can also be the result of an aggressive cache from your host (WP Engine) or CDN (AWS).
To troubleshoot this, I'll suggest the following steps:
1. Please make sure that WordPress, active theme, and plugins (especially Toolset) are all updated to the latest versions.
2. It would be interesting to test this with all non-Toolset plugins disabled and a default theme like Twenty Twenty-One.
If it's fixed, you can start adding the disabled items, one by one, to narrow down to a possible conflicting one.
3. In case the issue still persists, I'll need a clone/snapshot of the website, so that it can be investigated on a different server, without affecting the live website.
( ref: https://toolset.com/faq/provide-supporters-copy-site/ )
Note: We usually recommend the Plugin “Duplicator” (http://wordpress.org/plugins/duplicator/) for this purpose, but some hosts like WP Engine are known to block it.
For those hosts, you can create a backup file using the "All-in-One WP Migration" plugin:
https://wordpress.org/plugins/all-in-one-wp-migration/
Please let me know how it goes and I've set your next reply as private, again.