Bill Belichick's GF Jordon Hudson Fires Back at Online Critic of Relationship

Bill Belichick's girlfriend isn't taking any crap about her relationship with the famed coach ... calling out an online critic who tried to clown her about their romance.

Jordon Hudson posted a back and forth from her Instagram DMs to social media ... showing the hate a woman -- who goes by Abby Riley on the site -- threw at her about her romance with the 72-year-old coach.

In it, Abby asks her if she realizes her relationship is insane ... and, JH claps back by asking her if she realizes back that messaging a stranger "with the intent of harassing them with regard to their own personal relationships is insane, right?"

It's a pretty devastating blow ... and, Jordon doubled down on her response by adding a poll to the pic, asking if Abby's manners or punctuation -- she forgot a comma and a question mark -- is worse.

As you know ... Bill and Jordon's romance has received a lot of scrutiny since we broke the story about it last summer given the nearly 50-year age gap between the two.

However, the lovebirds clearly don't care about what everyone else thinks ... 'cause they've spent a lot of time together over the months -- including spending a sweet anniversary dinner together just last weekend.

BB's got a new job as head of the University of North Carolina football program ... and, Hudson's been hanging around the facility, sharing a pic of the field recently.

While they're not breaking up amid public pressure ... it looks like Jordon isn't going to take the critiques lying down.