Fellow professor here, enjoying the conversation. Lots of responses I agree with and think are convincing.
1. Your colleague is identifying that you and she and others in your peer group who are following you on Facebook have substantial privilege. (umm...duh?)
2. The problem, then, is what to do with that privilege. This will depend on your personal ideology and goals. If your colleague's goals are specifically to undermine and dismantle capitalism, and live in a way consistent with that goal, then there are other options. She can choose to not earn a salary for her work, or not work in a university (which is completely embedded in the wider capitalist society). She could choose to maintain her job and income, live on the smallest amount possible--in solidarity with whomever she feels is the least privileged or wants to highlight--and then redistribute the rest to organizations that she chooses who are in line with her goals.
That sounds radical, but there are many people who make that choice, including nuns, for instance.
If she chooses that route, which is morally impeccable in my mind, then she needs to decide how she will be supported once she can no longer work. For nuns, for instance, or those still living in gift economy societies, there is a non-capitalist institution or family support that is in place for those aging years. Or, she could make sure that she is comfortable living on the amount provided by SS, and be happy living a humble life.
In our mainstream society, though, there usually isn't much of a social safety net, which brings us back to the question of retirement and savings.
3. So if we *accept* the fact that we occupy a position of privilege in society, and don't have the courage to dedicate our lives totally to living outside the capitalist system of the community in which we are embedded, then we start looking at "next best" options. What kind of safety net do we provide for ourselves? What kind of safety net do we work toward ensuring exists for those less privileged? What kind of lifestyle are we morally comfortable maintaining? These are not black and white questions, but ones that always come down to personal circumstances and spending decisions.
I would agree with others here that "paying yourself first" means choosing to remove as much of your money as possible from the corporate, consumer economy, which seems reasonably aligned with anti-capitalist goals. How/where you invest it is another issue, of course. One of the principles of mustachianism (which may not be true for what you posted) is the idea of saving "just enough." In other words, saving enough to create financial independence, not wealth and money for its own sake. In fact, saving TOO much money, mindlessly, is ridiculed here almost as much as not saving at all. So, here at least, the goal is to save just enough to create your own safety net, by living modestly and not being a corporate shill, and then removing yourself from the capitalist machine where your job has been a cog in the wheel as early as possible, so as to devote yourself (if we look at Pete's example) to building community, ending car commutes, and spreading the anti-consumerism message.
You could point your colleague to threads like "what would happen if everyone became a mustachian?" where people are in fact very anxious about capitalism collapsing if everyone followed this path! :)
Though I know many academics who choose to live very simple lives in line with their values--and your colleague may be one of them--I think we're all assuming that she is actually doing the stereotypical thing and pointing the finger at "nyah, nyah PRIVILEGE" while not doing any of these thing. Just spending and feeling threatened by the idea of not spending, accepting a university pension, etc and occupying a pretty hypocritical position in real life. I hope that's not the case, but we've all seen it.