Let's look at this from two angles. One is the more fun, for me anyway, angle of "so you don't want to be tracked on the internet..." the other is the more useful, for you, angle of "no pictures on the internet".
Starting with the more useful angle. Unless you are a tinfoil hat wearing weirdo (which, hey, no offense if you are. Everyone is about something) then make a joke of it. How can you tell if you are a tinfoil wearing hat weird about this? If you can't shutup about it. I don't mean that in a mean way, I mean that if you can't graciously say "Nah, I'm not comfortable being in a picture" without also saying something like "THAT'S HOW THEY TRACK YOU!". Taking you at your word that you are not a tinfoil hat wearing weirdo - make a joke of it, be lighthearted about it, be willing to admit that this is socially unusual, in short 'be chill'.
What does 'being chill' look like? When someone bustles up and tries to set up the group photo gently decline. Say something like, "I know it's weird but I don't like being in photos. I'd rather sit this one out. I can take the photo if that would help!" Or make a joke of it, "Don't you know.... photos steal you ~soul~(spooky fingers here helps). Hand over the camera and I can steal your.. I mean take the picture."
For a variety of reasons I don't like having my own picture taken but, sometimes there's no getting out of it. I was involved in a fairly big research project(9+ universities across the US in a competition type environment). Team photos were required from the top down and if your name appeared on any research related to this or you were involved on the day of... your photo was getting taken and posted. Not just to Facebook but to newspapers and similarly. Additionally we were all told to give an interview for some sound bytes, again required from the top down, and, wouldn't you know it, I (the person who hates having her photo taken) was used on a fairly well known news site. The point I'm making here is that there may come a time when you have to decide if this is the hill you want (your career) to die on. If you / your lab makes some famous, world changing discovery are you going to be 'that guy' who refuses to get a photo taken? As unfair as it may be being difficult about something like that can harm your career and you should be aware of it.
To help with that awareness let's get to the fun(for me) angle. So you don't want to be tracked by companies? Your bank(s) are tracking your spending. If you shop at any major chain stores - those companies track your spending not only through your banking information but also through your loyalty card. Your TV and Internet habits are certainly monitored through your ISP and they use this to make choices about advertising and pricing. If you have student loans... good golly does Sally Mae and company sell your deets. A little more personally - Do you use Chrome? Gmail? Google Search? Does your school provide email services through Google? Do you have any of these synced to your phone or other devices? If so, Google has your life tracked. Other browsers aren't much better (though they tend not to have the handy hooks into your email) but any emails that aren't on a server you own or, typically, on a private(non-corporate email server) are being datamined and tracked in at least an abstract sense.
As a hobby of mine I like to see what kind of data I can get from public sources. I can get a lot of information just from your stackexchange profile. Searching your username I can find activity that matches both the time line and subject matter you have posted here which, with a little more work can get me an email address...
My point isn't to be all scary and creepy. Though, on reflection that is pretty creepy, my point is to talk, as one data scientist to another the desire to not be a 'datapoint' for companies is a valid one but it involves much, much more than not being on facebook. If being a datapoint is a concern for you you will run into problems in a research environment. If you publish or assist in publishing your name will be attached to the papers and it will be available in crawlable places. If you become a professor your name will be on your university's website along with a bio. When you enter the work force your name will probably be accessible in some way or form through your company's web presence especially if you are in a research/bleeding edge development or leadership role.
The decision to avoid having information on the internet is a valid, personal decision. The practicality and implementation of that decision takes a lot of reflection and work. This goes beyond 'I don't want photos on Facebook' but I would suggest that you schedule a time with someone in your field and/or your labs PI and talk to them about what that could mean for your career and how best to handle it.
