I moved to London in 1982 and by 1985 it was clear I was never returning as I no longer had family there. I continued to go to Alty games in London and environs but in those pre Internet, pre football being popular days it was hard to find information - it was hard enough to find out a result never mind any news.
As a result I had been going to random games every Saturday (there's a lot of teams to chose from in London) but eventually my partner (still my partner, Plymouth Argyle) said she would like to see the same team each week as then you get to know the players, what they can and can't do etc. We had a think and chose out local team West Ham, they were however chosen mainly because the atmosphere at UP was fantastic whatever the result. In he end I had a season ticket for 20 odd years and lots of good memories but eventually the matchday experience of the premier league ground me down and I found he only bit I was enjoying was going to the pub and seeing my mates before and after the game so we packed it in 4 years ago.
Luckily a few years before that I had discovered a group of fans who live in London and would go to Alty games so that's how I get my football fix now, unfortunately going to the pub is still the best bit of the day.
Anyhow to answer the question, I don't think it's a problem to support two sides who will almost certainly never play each other, if they did and even during the West Ham years I would support Alty.