The sentence as a whole is a stylistic train wreck. However, it doesn’t seem entirely out of the question to use the subjunctive here.
If we isolate the clause and take to take out of its passive form (to be taken), it becomes more defensible:
It is inappropriate that he take risks.
(I’m using he as a stunt agent here so you can clearly see that take is in its bare, “subjunctive” form.)
Here it is back in context:
. . . that does not mean it is inappropriate that he take risks . . .
And here it is back in the passive:
. . . that does not mean it is inappropriate that risks be taken . . .
Compared with the “impositive” adjectives on John Lawler’s sample list,* (in)appropriate feels less subjunctive triggering to me. Yet, appropriate’s synonym okay is on the list:
It is not okay that he take risks.
It is not okay that risks be taken.
*acceptable, advisable, all right, appropriate, better, crucial, desirable, essential, expedient, fitting, imperative, important, legitimate, mandatory, necessary, okay, optional, permissible, preferable, right, satisfactory, sufficient, urgent, and vital. Source: When should I use the subjunctive mood? @JohnLawler
Here’s a more exhaustive list of alleged subjunctive triggers. This one includes appropriate:

Source: The range of linguistic units: Distance effects in English mandative subjunctive constructions
So I could buy inappropriate as a subjunctive trigger. In my American English, though, I think it would be an unlikely sale. This would be more natural:
. . . that does not mean it is inappropriate to take risks. . . .