Hi,
Mag, from my days directing for the stage, I can tell you that too much of that anxiety is in your head a lot more than otherwise, and later you find ... ohhh ... it was alright!
My recommendations are nearly all the same as those above, with one exception. As a director, on the outside, you can see things that otherwise you folks playing (or acting) can not see from an audience's perspective, and there are some things that you can do to test that, and see how you react to it, and how you work in between.
So what did I do? George and Martha are arguing and a nut walks in with a vacuum cleaner. You have to maintain your concentration and not lose your spot, and yet, you have to handle the event. Easy enough ... Martha goes into a tirade about George's obsession with the maid ... (something like that) ... and after the vacuum is done with her 15 seconds, George throws the continuing line out, and generally, ADJUSTING, the mood is all that is required and this is not hard, if all the players (or actors) are listening to each other, and know how to get back in sync ... which can be discussed previously ... since you have no idea what the event will be! You can decided to say that the guitar does 4 to 6 beats in a particular scale, and that at the end, everyone is on par and tune.
Things like this, however, test your nerve ... because some folks panic and STOP. Do not EVER stop, and simply try to bring the others back, and the person in the group that is the best listener should be the one doing it, and the others should follow, and you can take turns doing this.
Eventually, after 4 or 5 times of this, you learn to trust your partner. At that point, you know it's not about "anxiety" as much as it is about LISTENING.
So, if you ask me, for a suggestion and clue? ... there you have it. How well you are tuned to the folks, instead of your instrument and notes (which is already memorized, etc, etc), you concentrate on making them better ... and the rest ... the more you do, the better will all of you sound and be!
Now take a break and go have a beer, or a smoke ... and smile. Then come back and rehearse again, and get someone to do anything else they want at any time, and try it again. Do not (ever!) duplicate the same event ... always try something different! And you will find, that listening, is the clue ... not anything else, because right then, you know what you have to do already!
Easy! So very easy!
BTW, I have never failed with a "beginning" actor or newby on stage, and would not fail either with a band, that was willing to learn and have fun! But the willingness ... is the issue, when folks end up thinking some stupid poop like ... that's not rock or jazz or some other BS! You miss the point totally! And it has nothing to do with the kind of music you are playing, btw ... that's "outside" the 4th wall!