If you have a long-term viewpoint (which is the correct viewpoint to have, in my opinion), then you should never worry about losing to "rags" or losing to some stupid random hand in a freeroll.
There's always another freeroll tomorrow! If you cannot realize and understand that we should ALWAYS want to be playing against "random" or "junk" hands, then you probably don't really understand this game very well.
Yes, we will sometimes lose with AA to 72o... but if you understand the math of poker you know that AA is only an 80% favorite over such a random hand, and that the random hand will win 20% of the time... but so what? Don't you want to be in such a good position as winning the hand 4 out of 5 times? Unfortunately, that is the best we can do in this game (at least in Texas Holdem anyway)... so we just have to learn to deal with it.
The best way to deal with it is to adopt a long term view. One day out of every five days you play a freeroll, you will lose a hand like this... but the other four days, you won't, and if you continue to play good hands against weaker ones, you will eventually win enough of them in a row to make a deep run and make a nice cash for yourself.
The problem is, everybody wants to win TODAY, right NOW... and sadly that is not a good way to approach this game. That is a short-term viewpoint and those who think this way are probably not in it for the right reasons, and won't last long enough to understand the point I am making here. Poker is all about the long-term, which is where our skill advantage eventually reveals itself. The short-term is all about the "luck factor" and we cannot control that on any given day...
Freerolls are awesome precisely because most players are not playing good enough cards, and this gives those of us who DO play a bit tighter a distinct advantage in them... but only over the long run!! Hope this helps, best wishes.
P.S. I also do not deposit to online poker sites, but since I love the game, I decided to make a very fun challenge for myself, which is precisely why I joined CardsChat... my challenge is to win a few bucks in the freerolls here, over time, and then use those couple of dollars to try and win even more in the regular tournaments... so far my challenge has been quite a success, I turned a dollar or two into a four-figure bankroll on one site, and I'm at low three-digit bankroll on another smaller site. This challenge has cost me nothing, and while I probably won't ever see the money (because if we don't deposit, the sites make it quite difficult to withdraw the money and I'd rather just not get involved in the hassle of bitcoin wallets and all that crap), but I really don't play this game to get rich, even tho that would be nice if I did.
I play this game for the challenge and for the fun of it. So I offer this as a suggestion to you - but realize, it won't happen right away, it takes time and much patience to conquer such a challenge... but this is precisely why I love poker so much, because nothing good ever comes easy! Good luck.