John Henry and his wife, Linda Pizzuti, over in Liverpool.
The simple answer here is yes, John Henry owning Liverpool FC will most certainly affect how he deals with the Red Sox. I've been bouncing this around in my head for a bit now, and that's the only logical conclusion I can come to, I mean, how could it not? I'm not naive enough to think that John Henry didn't own other businesses besides the Red Sox, however, he didn't own a commodity so similar to the Sox as Liverpool FC.
I think one of the main reasons Red Sox Nation as a whole is displeased with the purchase is because of how similar the franchises are to each other. They both have extremely passionate fan-bases, both have rivalries with larger markets, and both have rich traditions. As little as most Sox fans know about the Premier League, they recognize first and foremost the passion Liverpool fans have - and they see a lot of themselves in that passion, thus are threatened. This is an understandable reaction, and is taken directly from the "Step Brothers" playbook, however, I don't ever see us (the two fan bases) becoming best of friends.
What us Sox fans have to remind ourselves is that John Henry is not, nor was he ever, a Red Sox fan. The sooner we come to accept that, the sooner we can accept this purchase for what it is, a business decision. I mean, Liverpool isn't even the first franchise competing for Henry's attention, that honor would go to Roush Fenway Racing. But I believe NASCAR is something so left field for most North East baseball fans, that it was something we scoffed at, and didn't look at as a rival. We couldn't see the similarities, but they're there as well, especially the passion amongst the fans. Which again brings me back to Henry.
Before owning the Red Sox he was a partial owner of the New York Yankees. That right there should be all you need to know about how Henry feels about sports ownership. He has no loyalty to a particular franchise or town, if that franchise or town isn't going to return him a healthy profit. He wasn't helping save Fenway Park because it was a national treasure. He was saving it because it would make the ravenous fan-base happy, and in return, make him more money. That, and it's a heck of a lot cheaper to add some Monster Seats then to go through the political hoops and money needed to build a brand new stadium. 
Like everything Henry does, it was a calculated business decision. Bill James isn't on the Red Sox payroll because Henry loves baseball statistics, he's on the payroll to make his investment return a maximum amount of profit, Henry is a numbers man after all, and winning returns dollar signs.
There's a lot of Liverpool fans that dislike this purchase with as much passion (there's that word again) as Red Sox fans. Thankfully for both fan bases, Henry's pretty good at what he does, and he usually places the right people in the right postion to succeed. Just don't fool yourself into thinking he's on the same ownership level as Robert Kraft or George Steinbrenner. Both of whom were also crude businessmen, but were also true fans of their teams and game. Unfortunately, for Red Sox and Liverpool fans, Henry is just a crude business man, and that'll have to be enough, as long as they win.
