No. They are free, libre and open source, anybody can pick up a piece of code and run with it any way they want. That is the whole idea.
I think you are asking, should the wider society care more, even to the point of getting involved and working to improve the code they use? Here the answer is yes, yes and yes.
In particular, major organisations such as governments, big business and international charities need to put riders on their supplier contracts to provide a commitment to software security support. If every such body put just one employee full-time onto identifying and fixing security flaws in the FOSS they use, it would make a huge difference. It would also repay those bodies a thousand times over on reduced costs of dealing with compromises.
"Klinger, do you know how many zoots were killed to make that one suit?" — BJ Hunnicutt