I've gathered he's a fan of some of it - there's certainly some fond reverence for 60s Trek, they were delighted to have people like Walter Koenig and Majel Barrett drop by - but there was a bit of a fandom war between B5 and Trek (DS9, mainly). There are various stories about who did what to piss off who - a longstanding story was that JMS had pitched his idea to Paramount, who'd turned him down then went and made DS9 (you get lists of similarities like 'the station is next to a wormhole/jump gate' and 'they get a warship partway through'), although on the other hand, as well as being fans of Walter and Majel and the like there's plenty of anecdotes of the B5 and DS9 crews actually respecting one another's shows at the time, so I feel like it was more a fan thing than something from the creators themselves. Seemed pretty bitter at the time, although I guess nowadays it'd just be par for the course.
JMS does have trouble walking away from the chance to tweak peoples' noses though, so you get bits like the Lumati, or Ivanova complaining "We're not some deep space franchise, we mean something!" (although I believe that was Peter David's line, JMS just thought it was hilarious and left it in). Stuff like that didn't exactly help damp down the flame wars going on while the shows were airing - and it's worth remembering that JMS was very active online all throughout production, which as well as making for a treasure trove of background information on the making of the show, also put him right out in the open for Trekkies with a superiority complex who couldn't wait to point out, directly to him, how B5 was just riding Trek's coattails, which you can imagine would be irritating when he nearly literally sweat blood on a daily basis to make B5. There were moments he came off as maybe a bit more vehemently defensive of B5 than needed, but you can hardly blame the man.