If there is such a thing as a girl’s team, there is no justification whatever for a mixed team - only a boys’ team. There being no question of allowing boys on the girls’ team.In this case they don’t have a girl’s team, but they presumably don’t have mixed competition to play against.
That said, in competitive leagues there should be no question of allowing boys on the girls' team -- while girls on the boys' team may be ok -- because players can "play up," but they can't "play down." This is common in youth sports in age-defined competitions and in tiered leagues with defined divisional structures, but I think the same principle can (and sometimes does) apply to girls playing on boys' teams.
(In rec leagues, girls play successfully with the boys in the earlier years; then puberty hits and most of the girls can't keep up; very few can hang in with the boys into the high school years. In areas with well-developed youth programs, most of the competitive girls will have migrated to girls' teams and girls' leagues before that happens.)
"Playing up" is ok because a girl does not gain an unfair competitive advantage by virtue of being a girl. Some leagues are quite accommodating on this, especially if a particular club does not have a girls' team at some particular age level. (E.g., the girls' team folded at U15 because too many of the girls, now in high school, moved to other activities; a handful are left and want to keep playing soccer, so the club puts them on the appropriate boys' team.)
The gender benders, of course, turn this principle on its head and insist that boys who want to pretend to be girls should be placed on the girls' team. The problem, of course, is that the boys in this situation DO gain an unfair competitive advantage; in gender terms, they are "playing down," which you can't do in any legitimate league. It doesn't matter if there is a big tournament or heated rivalry game coming up: varsity players can't step down to the JV; U17 players can't moonlight with the U14s; Division 1 soccer players can't play for a Division 5 sister team in the same club.
A very few girls playing up on boys' teams is not the same thing as a coed team/league. There are some recreational leagues that blur the difference; they are nominally coed but the reality is that most of the girls have dropped out, and only one or two girls are still playing for what is, in reality, a boys' team. In a real coed league, you need quotas for the girls, with both teams fielding similar numbers. This produces an elaborate game within the game. Years ago, I coached a team in a very competitive adult league playing coed touch football. We became a very good team, with a number of ex-college players and the rest of the guys being pretty good athletes as well. The challenge was always to use offensive and defensive schemes that matched our girls vs. their girls, and the guys vs. the guys. You certainly couldn't afford to get caught in a mismatch where one of the girls got isolated in coverage against one of their guys.
Ah, memories. This changed for us in a big way when one of the athletic guys brought his girlfriend who had played Division 1 college basketball, and she brought one of her former teammates. They were good, not quite as fast as the guys (and they would not have survived in the tackle version of the game), but very competent all-around athletes. You would want them on your adult rec football or softball team, and not just to make your quota; they more than held their own. When you get a couple of girls who can run with the guys in a coed league, you will blow most other teams away, and we did.
There are too many posters on this thread treating this as a ritual purity issue. This is not about a trans-whatever trying to impose its fantasy on everyone else. This is just a girl whose team disappeared and who would like to keep playing. If she can run with the boys, I'm ok with it. If she's not good, she won't get playing time. That's ok. If she is good, some of the boys might get shown up by a girl. That's ok too.