Personally, I opt for the grope: it isn't much of a choice but I get exposed to enough radiation during the ensuing flight and I like being able to pick who gets to see my white bits. These two issues are nothing compared to the more subtle aspect regarding the systematic invasion of our privacy. The right to our own bodies and private discourse via telephone and internet is eroding. Privacy is a basic right as stipulated in the fourth amendment of the US Constitution and upheld by decades of court proceedings.
The real issue is, "why". It is easy to take the path of least resistance, as redundant as it sounds. If you say to yourself, "I feel safe, so why should I care that other people think our rights are being violated?" then this is about you.
We all benefit when a marginalized group is protected and lifted closer to the playing field. History is painted with broad strokes showing how this is true: I'll give two examples.
In the 1930's Turkey gave full rights to women: it was unpopular and caused social upheaval as the patriarchal culture resented women approaching the status divinely afforded to men. But within the next few decades, as women entered the workforce, even though their job opportunities were limited and many women were still sequestered at home, their inclusion in the economy contributed noticeably to the sudden jump in productivity and increase in the GDP. Whole families had more money for their food, clothing, and education. As more women received a compulsory 8 year primary education, fewer men were required to perform administrative tasks and were freed to engage in higher pursuits. Women still struggle for equality with men in Turkey but everyone benefited from the attempt to level the playing field, not just women.
This next example is more subtle but the benefits were just as profound.
In 1979, Sweden passed a law that made hitting a child a civil offense. This was also an unpopular political move as parents struggled to raise their children without spanking them. The benefits became clear within a decade as the rates of child abuse dropped 80% and within twenty years the rates of children entering foster care dropped to almost zero. The sheer magnitude of economic gain in all but eliminating the need for state care of foster children is nothing compared to the tangible good as indicated by drops in child abuse and displaced children. The bottom line is clear: everyone benefited from taxpaying adults to the most innocent.
So you might ask, "so what does women working and corporal punishment of children have to do with TSA screening techniques?" Well, this is another issue that might take a few years to manifest it's detrimental effect. Imagine how much tax money goes into maintaining the machines and the time lost using them and accommodating those who opt out. How about the deterrent effect on the ailing air travel industry. Think about the cost of care borne by individuals as the rates of cancer increase. Where would it end: travel by train, bus, light rail, and toll road might soon include an electronic strip search and grope festival. We might not be able to shop for groceries or head to the mall with a lighter in our pocket. Most disturbing of all, consider a child who grows up thinking it's okay for an authority figure to take naked photos or grope that child's clothed body.
The fact of the matter is, our rights are violated by the search techniques enacted by TSA, the Patriot Act and Department of Homeland Security. If you still say to yourself, "I feel safe, so why should I care that other people think our rights are being violated?" consider countless Germans who told themselves the same thing starting in 1933 and how many people suffered and died because good men did nothing.