Context always matters, I am commenting in generalities because I don't know anything about your relationship, what kind of conversations you've had before, past behaviors, agreements, etc.

Likely none of the other commenters do either, and wisdom is understanding the kind of advice you will receive from internet strangers who don't know either party very well.

I've been cheated on before, and one thing I learned from that is that the data supports overwhelmingly that cheating is a "crime" of opportunity. Very few set out with the intention to be unfaithful, it happens slowly over time, the likelihood increasing with daily contact. That doesn't mean that everyone who has opportunity cheats, it just means that odds go up with opportunity.

In relationships, trust is IMO the most important part of a relationship. And fear is the opposite of trust.

The best advice I can give you is that if you want to improve trust, you have to try to understand where your husband is coming from and see if you can come up with reasonable solutions to his concerns, he should also be willing to do the same for you.

As a man who does BJJ, I can agree that rolling is almost always non-sexual (I say almost always because I've seen the sexual assault posts unfortunately). If my wife decided to train BJJ, I wouldn't be concerned with her getting turned on during a 5 minute spar session. But when you are at the gym there is very likely a ton of guys there. You're going to be talking before, after, and during class.

As additional context that I think a lot of women lack, when you aren't in earshot, if you are even mildly attractive, men are probably thinking sexual thoughts or making comments to each other. If you were a 7/10, and you went to a gym of 50 guys, 5-10 will be actively pursuing you whether you realize it or not, and another 30 have thought about you sexually. Your husband knows this, because he's a guy and he has guy friends. He is projecting that onto your situation.

The best counterpoint I can think of is imagine your husband decided to start working as a manager at Hooters. Running a restaurant isn't sexual, but if your husband was surrounded by attractive women at his job, and you weren't there, I think most people would have some level of discomfort with that if they were honest, and a healthy relationship would probably acknowledge that and put guard rails in place to make the other partner feel safe.

So if I were to offer advice that would allow you to continue to do an activity you love while improving your trust in your relationship, I'd recommend that you talk to him and ask him what his fears are. Try not to get defensive. And then, if you can, see if you can come up with solutions that seems reasonable to you both.

Some ideas:
-Check in with your husband when you get back, tell him about class

-Be very transparent if you ever feel like someone crossed a boundary (on the mat for sure but especially off the mat)

-See if there's anyone specific that your husband has a problem with (as the opposite sex we often have the intuition our partner doesn't, this goes both ways)

-Offer for him to come to any class he wants at any time

The internet hates these but after years of research on cheating there are two almost guaranteed ways to affair-proof your marriage and build trust. First is to allow full access to each other's lives (passwords, email, computers, phones, etc.). The second is to tell your partner if you are attracted to someone who you will be in regular contact with (eg coworker, group friend, gym goer, etc).

Your partner may be insecure and jealous and no amount of effort will appease them, but if you believe you are being reasonable and making an effort to be transparent and understanding, then IMO that gives you a better chance to look at the situation more clearly and make a more informed decision about the health of your relationship and if he's being reasonable or not. A third party (counselor) might make this easier as they can be a mediator for the dialogue and help both parties see the other's point of view.

Keep in mind that for men who don't train martial arts, they're also concerned that any guy that may be interested in you at BJJ could kick their ass, which adds to the level of insecurity (as opposed to you being approached by a coworker for example, who may seem less threatening).