There's no particular reason to believe Enterprise is non-canon. It was created by Rick Berman and Brannon Braga, who were at one time showrunners of The Next Generation, Deep Space Nine, and Voyager.
In-universe, we can connect Enterprise to almost every other definitely-canon Star Trek property:
TOS: The fourth-season Enterprise two-parter "In a Mirror, Darkly" is a sequel story to the TOS season 3 episode "The Tholian Web", and a prequel to the season 2 episode "Mirror, Mirror".
TNG: In the Enterprise series finale, "These are the Voyages...", Commander Riker is interacting with a holodeck recreation of the Enterprise crew in order to help him sort out an internal conflict, part of the seventh season TNG episode "The Pegasus".
DS9: Aside from the fact that being connected to TNG automatically connected Enterprise to DS9, the Enterprise episode "Acquisition" introduces us to the Ferengi well before their official first contact in TNG. In the episode, a Ferengi named Krem is educating Captain Archer on the Rules of Acquisition:
Krem: Never allow family to stand in the way of profit.
Archer: Another of your rules?
Krem: Number six.
Enterprise Season 1 Episode 19 "Acquisition"
Meanwhile, in "The Nagus", Quark quotes the Sixth Rule of Acquisition as:
Quark: Never allow family to stand in the way of opportunity.
Deep Space Nine Season 1 Episode 11 "The Nagus"
First Contact In addition to James Cromwell reprising his role as Zefram Cochrane (in a cameo), and a blink-and-you'll-miss-it glimpse of the Phoenix (see the Into Darkness entry, below), the events of First Contact are referenced by Captain Archer, remembering a speech made by a very drunk Cochrane:
Archer: When I was a kid, I read everything I could about him. It took me a while, but I finally found it in the database. He was giving a commencement address at Princeton when he started to talk about what really happened during First Contact. He mentioned a group of cybernetic creatures from the future who tried to stop his first warp flight when he was living in Montana. He said they were defeated by a group of humans who were also from the future.
Star Trek Enterprise Season 2 Episode 23: "Regeneration"
Star Trek (2009): When Spock and Kirk first encounter Scotty on Delta Vega, Scotty tells us how he came to be stuck with his less-than-enviable assignment:
Scotty: Had a little debate with my instructor on relativistic physics and how it pertains to subspace travel. He seemed to think the range of transporting something like a...like a grapefruit was limited to about a hundred miles. I told him that I could not only beam a grapefruit from one planet to the adjacent planet in the same system - which is easy, by the way - I could do it with a lifeform. So, I tested it out on Admiral Archer's prized beagle.
Star Trek (2009)
Emphasis mine. As discussed in another question1, this is Admiral
Sam Beckett Jonathan Archer, and Porthos from Enterprise
Star Trek: Into Darkness: Admiral
Robocop Marcus has a bunch of model air and space vehicles, from the Wright Flyer all the way to his own USS Vengeance:
I took this screenshot myself, so apologies for the blurriness.
On the far right is clearly the Phoenix, Zefram Cochrane's warp-capable missle, from the movie First Contact and the Enterprise title sequence. It's hard to make out, but I believe the middle one is the NX-Alpha, the Warp-2 prototype that appears in the Enterprise episode "First Flight" (Season 2, Episode 24). The one on the far left is clearly the NX-01 herself.
QMx, the company that made the models, confirms my suspicions on their website. They have a gallery of the 14 miniatures they made for the movie, one of which is the NX-01. Although it looks slightly different from the show (the two-tone hull plating, for instance) it's unquestionably the same design.
Here's a thumb of the NX-Alpha model:
And a high-res of the NX-01 model:
Star Trek Beyond: Captain Balthazar Edison is described as having been a MACO before the Federation was founded (and the MACOs disbanded). He later reveals that he fought in the Xindi campaign:
Edison: I fought for Humanity! Lost millions to the Xindi and Romulan wars.
Star Trek Beyond (2016)
Both the MACOs and the Xindi campaign were fixtures of Enterprise's third season.
Discovery: Among a handful of background references, several mid-season episodes of Discovery make a plot point of the USS Defiant's presence in the Mirror Universe, something that was initially established during the Enterprise two-parter "In a Mirror, Darkly."
As well, in her speech to the Discovery's crew at the end of "The War Without, The War Within", Admiral Cornwall references Archer's visit to Qo'noS from the Enterprise series premiere.
Although the show wasn't as broadly well-received by Trek fans as some of the others, as far as I know no significant portions of the fanbase have rejected it, and it's never been officially rejected by Paramount, as TAS once was2. In fact, the NX-01 Enterprise is listed on the database at StarTrek.com, as close to an official canon repository as I can find.
The only reason I can think of to exclude Enterprise from canon is if you're only considering things made with Gene Rodenberry's direct involvement. If that's you, then disregard the above.
1 Disclaimer: I have the top-voted, accepted answer on this question
2 Although this decision has since been reversed. TAS episodes are listed in the same database on StarTrek.com