I fall into this category. You've asked the question, so I'll give you the answer:
When I started getting interested in football, I didn't even know my local club existed. None of my family had any interest in football whatsoever, so the only way I got to see it was on TV... usually The Big Match on ITV or Saint'n'Greavsie, stuff like that. For whatever reason I latched onto Arsenal (this was in the late 80s when I was about 8, before they won the league in 89) and from then on they were my team.
Now, the reason I have a soft spot for my local side is down to a few reasons. First of all, because of the 'snobbery' in football, there are always people out to put you down if you don't support your local team. It's that trump card people like to keep up their sleeves for when they are being decimated in an argument... "well, at least I'm a REAL fan, going to support my local team - not a glory hunting armchair fan like YOU". So they look a bit of a muppet when I say that actually I do go to watch local teams - I'm still an armchair fan at heart, not a hardcore supporter, but because of their misconceptions about me the attempted insult doesn't hit home.
But more importantly, heck, I just like football, and when I go to watch Salisbury occasionally it's just a case of rolling up and paying at the turnstiles, guarenteed to get in even when there's a huge gate. "We" won the league this season (10pts clear with 2 games left) and that's something to feel proud of from a local side, looking forward to the Conference South next season. Likewise Southampton is the nearest League club to me so I've been to a few of their matches in recent years as it's not too bad from a travel/ticket availability front. Don't really care much about what happens to them though.
Going back to the original question, I reckon people can do whatever the hell they like. People say you can't support two clubs, but why not? Who are they to dictate what the personal feelings of another individual are? There are some people who give two clubs far more support than other people give to their single club. I don't support different teams equally, but that doesn't mean to say that I look down on others who claim that they do.