If you get so insecure with your woman that you feel the need to end the relationship over her getting tacos with one of her guy friends, you're beta yourself. However, if the guy's obviously alpha, handsome, and does well with women, an alarm should definitely be going off.
Personally, I'd just stay aloof either way. It's not like me putting my foot down and telling her who she can and can't see is going to make things better. I know this from personal experience cause it's how I lost my last girlfriend.
I was pretty sure what was going on even though the dude was her best friend's BF.. I did the typical "It's me or him" shit, talked shit about him having STDs, etc.. All it did was make my GF hate me even more and probably gave him the "give him something to be mad about he thinks you're doing this anyway" green light.
If the guy's actually a beta orbiter, your alarms naturally won't go off given you don't have anxiety issues or something. Because you see him as harmless and you could easily beat his ass (obviously you shouldn't but you get my point) for acting out of line. If anything he gives you a break and plays therapist for your woman and goes shopping with her so you don't have to.
The key to staying in frame in this situation is always ABUNDANCE. Realize she's not your only option, she's not some special little angel and there's plenty of fish in the sea. It's just your turn. Maybe hangout with a female friend if you want and it might dread her into not going out with that guy.
Another thing to consider is to "keep her entertained" yeah it's a lot of work, but you gotta do what you gotta do. Plan fun stuff with your woman, nice dates, dinners etc.. Invite her to do cool shit with your social circle. If she's doing this, she's not gonna be too concerned to get tacos with chad cause she's doing fun shit with you and your friends all the time who are way more exciting.
Situations like this could be nothing or could be relationship enders. Just accept the outcome for what it is and keep living your life. Who gives a fuck if you get cheated on.. Happens to everyone. Suck it up and move on.