There is another topic that is similar to this one, you may have something in common. http://support.advancedcustomfields.com/forums/topic/5-3-6-upgrade-issue-not-displaying-some-fields/
I reverted a site to 5.3.5, added fields and values like the ones that are having problems with (post object, image, etc) and then updated to 5.3.6. I’m not seeing any issue.
What other plugins are you running? theme? You’ll need to narrow down where the conflict might be by disabling plugins and possibly trying on one of the default WP 20XX themes.
This appears to have something to do with fields that save ID values, not that I know what that might be.
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