As the term "hugbox" has not, as of yet, been entered into the Oxford English Dictionary or Webster's, "groupthink" appears to be the most appropriate synonym with the definition closest to that which is most commonly implied by use of the term "hugbox."
That said, the matter of either of these words, or any word, being more or less offensive is entirely subjective, varying from individual to individual. While you may wish to take this into consideration for diplomatic reasons, concise communication of thoughts and ideas is the goal of any language.
Although it is probable that either of these words would be found offensive by people who fit the definition of being in a hugbox or influenced by groupthink, as the very nature of such implies that these individuals bear a strong resistance to challenging ideas—including the very idea of accepting that one is in a hugbox; you must choose for yourself whether to place a higher priority on reaching communication with someone or else forgo your attempt to reach an understanding because you feel there is a risk that the individual(s) you are speaking to are not also willing to communicate.
It is important to differentiate between communication and being insensitive. There seems to be a lot of confusion between the two and you really do not have to sacrifice your willingness to communicate or use the English language. Communication involves two or more participants and each participant is entirely responsible for their decision to participate. You do not have the ability to make this decision for others. Nor do you have the right.
That we have agreed to definitions attributed to words is what makes this form of communication possible. The best that you can do is adhere to the language while conveying your thoughts to others. In doing so, you offer them the opportunity to do the same. If they choose otherwise or for whatever reason are not able to do so, then you must accept that it will not be possible to communicate with such people by means of language.
So as "hugbox" has become a popular term with meaning similar to that of "groupthink" (although differing in its usage because a hugbox is generally used in reference to the group or setting itself), I am casting my vote in favor of using the original term "hugbox" if you feel that it most appropriately conveys your message.