I would rate this as fairly plausible. A related story from the Bush era:
During Bush's tenure, the White House's IT department blocked sites like Facebook, YouTube, Twitter, and most of MySpace. The ability to comment on blogs was blocked, as was certain content that was deemed offensive. According to David Almacy, who served as Bush's director for Internet and e-communications from 2005-07, only two people had access to the iTunes store during that period: Almacy, who had to upload speeches to the site, and the president's personal aide, so that he could download songs for Bush's iPod.
The restrictions seem draconian by today's social-media-friendly administrations. I can't see porn access being much more useful for gov't business today than it was then... so there's little reason to think that part of the restrictions would have been lifted. On the other hand if the Commander in Chief insists enough... who knows what changes are likely.
The same source I quoted above said there was no Wi-Fi at the White House back then. I do wonder if there are any 3G/4G wireless internet restrictions (jammers/blockers or hijackers--there are stories that some are present in DC); if not then the restriction(s) are limited to the actual White House equipment... However this might not help Trump much; a 2013 story said that Obama was not "allowed" an iPhone. I'm not sure if that changed thereafter, or if if simply matter of recommendations vs. actual restrictions. A 2016 story said Obama (finally) received a very locked-down smartphone:
After he got the phone, the president was told “this is a great phone, state of the art, but it doesn’t take pictures, you can’t text, the phone doesn’t work, you can’t play your music on it,” Obama said, laughing along with Fallon. “So basically, it’s like—does your 3-year old have one of those play phones?”
A 2017 NYT story said that Trump was still using a Samsung Galaxy S3 (to tweet at least)... A later story said he he had switched to an iPhone for tweeting... but there were conflicting reports whether that mean he had changed his phone or if someone aide was typing his tweets from iPhone. Another story says Trump is only using his S3 as a pager nowadays.
Also, a recently (2018) implemented change in White House policy:
After explosive excerpts from an upcoming book on the Trump administration were published earlier this year and reports noted that author Michael Wolff taped interviews, the White House finally banned staffers in January from using their personal cellphones as it said it would do in 2017. [...]
After it came to light that [Chief of Staff Gen. John] Kelly's smartphone was hacked by potentially by foreign operatives, the Secret Service reportedly put the kibosh on personal devices in the West Wing.
This seems not to apply to the "higher-ups", but it's unclear where the line is. And what seems to be latest story on the president's phones:
The president uses at least two iPhones, according to one of the officials. The phones — one capable only of making calls, the other equipped only with the Twitter app and preloaded with a handful of news sites — are issued by White House Information Technology and the White House Communications Agency, an office staffed by military personnel that oversees White House telecommunications.
While aides have urged the president to swap out the Twitter phone on a monthly basis, Trump has resisted their entreaties, telling them it was “too inconvenient,” the same administration official said.
The president has gone as long as five months without having the phone checked by security experts. It is unclear how often Trump’s call-capable phones, which are essentially used as burner phones, are swapped out.
While none of these phone stories is about porn specifically, it's clear that there's a strong drive, at least by his security staff, for him to limit his internet access... which does indirectly support the idea that he would inconvenienced in other ways by IT/security staff.
Finally, it seems that while Trump writes on the internet a lot, he reads it much less, preferring TV and printed newspapers instead. So it might be that his alleged complaint might be in regard to the channels provisioned. I couldn't find anything specific in this regard, alas. What I could find was that Trump watches a lot more news on TV than his recent predecessors. He also said he has the “the world’s best TiVo” at the White House, but it's not very clear what he meant by that.