Word for "to make changeable"
In a comment, I offered up the term unfrozen, and all forms thereof as a word meaning "having become able to be changed." I was initially worried that this would be too jargon-y for the questioner, however, he has made it clear that it will work.
I would generally use the term for things such as files, bank accounts, records, etc. However, there is no reason I can see that it couldn't be used in a more general context. The dictionary offers the following definition:
To remove a control or restriction on (prices or wages, for example).
This lends toward my instincts. In your case, I still think opened would be best for the first. An "open mind" is what one would generally say about someone whose thoughts have become more liberal. Unfrozen, however, is perfect for the second and many other uses.
I'd say "opened" would work for the first example. For the second example "opened" would perhaps confuse.