1. In SA YD 1:1 and in the underlying Beth Yosef, the m'chabeir sees no reason not to permit women to do Sh'chita. [Lo ra'inu eino Raya]In fact such Halachic permission is granted in Hullin by the Mishnah and the G'mara
Rema based upon [iirc kol bo and agur] says "she'ien l'haniach nashim lishchot". Shach there defends this Rema
Note - We have here a principle that what is Halachically permitted can still be restricted by "ein manichin" or similar language.
2. The m'chabeir himself use this same terminology as this With Regard To consecutive aliyot involving EG 2 brothers. See SA O"Ch 141:6 and the Lashon "y'cholim...v'ein manichim"
3. I found an early source in Mishnah Yoma 6:3 for this terminology viz. of Halachicallly permitted but "lo hayu manichin" With Regard To who takes out the s'ir hamisthalei'ach. There the B"D of Kohanim [Bartenura] legislated a higher standard than the Halachah. And an exemption was noted for "Ars'la"
For Further Research:
1. Are there more sources on these cases - especially those giving us any parameters?
2 Are there more cases in Sha"s and Poskim
3 What might be the parameters justifying exemptions?
4 Does EG Encyclopedia Talmudit or others define the parameters of this phenomenon of "mutar aval ein manichim"?
Comment: it does not take an Illuy to see that Traditionalists will likely defend the Agur/Rema/Schah on SA YD 1:1, while "feminists" will seize on this opportunity to promote women since it complies with "Halachah".
What bothers me I guess is that SOME on the left have impugned the Rema et al. as somehow doing something aweful, although we see that it is a policy rooted in Sha"s in other circumstances.