While my area of expertise didn't deal with cell phone towers in particular, I did deal extensively with land mobile radio at 800mhz which is pretty close to where most cell phones are. Bandwidth is not necessarily the issue, ERP (effective radiated power) is. The cell towers that I've looked at are effectively omni-directional; look at the antenna arrays - they go around the tower in a circle. Now perhaps those antennas are servicing more than one cell in different directions at different times but during any peak usage time, they're all likely to be transmitting. Even if what I'm referring to are mostly receive antennas, there are enough transmit antennas to do what's required and the fact that they're directional isn't reassuring if they happen to be pointed at me. Even though as cells get smaller, the power required to accomplish the same thing goes down, they're designed to blanket a particular area with whatever power level is required. Obviously, the further you are away from it, the less you're exposed to and it's exponential (presuming you don't wind up getting closer to the next cell...). Because of the radiation pattern, I would rather live directly underneath the tower than half a block away. That goes for television/fm transmitting antennas as well.
By the way, for those lurking, I once lived in a town that had a fit over the installation of some satellite uplink antennas. Dishes are scary (I guess...) Satellite dishes typically have a 2 degree or better directional pattern and they're pointed up in the air. They do have splashy side lobes of radiation but at a much reduced level (think of the reflector in your flash light). What the people in this town didn't know is that those satellite antennas were sited right below a UHF television transmitting antenna with an ERP of over a million watts. You could almost walk around like Uncle Fester with a light bulb lit up in your mouth thanks to that TV antenna, but those little 200 watt satellite antennas were new so they were scary.
People also don't realize that they're exposed to a constant level of microwave radiation from satellites (at least while they're outdoors) - and it's getting worse all the time. Back in 1980 there were only a few non-military satellites and they were running 5 watts with not-that-good antennas. You needed a 15ft dish to get a snowy picture. Granted today receiving technology is better, but satellites now pump out 40 watts on each "channel" with very good antennas and there are ____loads of them raining down on you. By the way, did you vote for that? ................ Maybe with your wallet - anyway...... I know folks in the industry who unlike me now , make a living at that business who are concerned about it. These are hardly the type of folks to don tin-foil hats - believe me.
An interesting sidelight (no pun intended). I was told by a military radar tech (fighter planes) that one of the standing jokes for the new guys on base was to order them to go get an arm load of 48" flourescent light bulbs. On their way back from where they got the bulbs they would walk several hundred feet in front of a fighter and one of the old timer wise guys would fire up the radar in one of the jets causing the armload of light tubes to light up! Needless to say there was a broom handy.
The term "any consequence" is relative. I don't know what the consequences of constant, low-level exposure are. Until I do know, I would prefer to err on the side of caution. That doesn't mean go berserk, it means given a choice, I would prefer to avoid it.