I have spoken with the music director. She ihas nothing ahainst female solos either, though she does know some priests who are not.
I'm not trying to pick any kind of fight here, or be contrary. I say that only because somehow discussion of music and the rules often seems to result in people taking matters personally. That is most certainly not my intention. Since you asked for help here, I am trying to provide you that and also, given my expertise in Sacred music promote what the Church has said She wants, through her Popes.
That said, I assume you mean the music director told you she knows some priests who are "against female solos", since before you wrote that the pastor did not suggest that having a woman to sing was a problem.
Unfortunately, I think you're dealing with a priest who does not know the Church's rules on music, since he raised no red flags on any of what you wrote here. From your comments, I would think that the music director also is either ignorant of the rules or mistakes them as mere recommendations or the unfortunate tastes of some. I have only your recounting to base these comments on, so perhaps I am incorrect.
The problem is not as much with women singing in Church. The problem is with solos. Pope St. Pius X clearly restricts solos in his Instruction on Sacred Music (which he says he gives the "fullness of Apostolic authority and ... the force of law"):
By this it is not to be understood that solos are entirely excluded. But solo singing should never predominate to such an extent as to have the greater part of the liturgical chant executed in that manner; the solo phrase should have the character or hint of a melodic projection (spunto), and be strictly bound up with the rest of the choral composition.
So solos are not completely forbidden, but if an entire selection is a solo composition, then at the very least its liceity is questionable. This is also why it is illicit for one person to sing the Propers (outside of grave necessity).
The other problem for most (non-liturgical) solos is that most are Operatic arias which have been converted to religious songs. The operatic style, and much of the popular 19th century songs are simply inappropriate for use in the Church:
Among the different kinds of modern music, that which appears less suitable for accompanying the functions of public worship is the theatrical style, which was in the greatest vogue, especially in Italy, during the last century. This of its very nature is diametrically opposed to Gregorian Chant and classic polyphony, and therefore to the most important law of all good sacred music. Besides the intrinsic structure, the rhythm and what is known as the conventionalism of this style adapt themselves but badly to the requirements of true liturgical music.
While St. Pius X does exclude women from singing in the Church, since it is a clerical office (like an acolyte), in the late 1950s, it was tolerated to have a mixed choir if it was truly impractical or impossible to have an exclusively male group. Given that in most places an exclusively male group for both the Proper and other selections (polyphony, etc.) is not available, it would seem that it would be tolerated in most places for women to sing in the choir. With as good as our men are here where I direct the choirs, we still are not of sufficient number or quality that we could sing the high-quality polyphony we sing without the help of our sopranos and altos. While I continue to develop our male talent, for the foreseeable future we'll have mixed choirs. Because I know that we are one of the top choir programs in the SSPX and we must use this exception, I don't expect that most places would be able to fulfill the rule of St. Pius X on men as singers.
Again, none of this is intended to attack your or anyone involved here, merely to provide you all of the information, since it seems you're not being told the whole story regarding the Church's rules on music.
On a different note, may I thank you (on behalf of music directors everywhere) for working on music so far in advance. Unfortunately many parishes, but especially ours, have a problem where everything in planned last minute. I rarely get even a month's notice, let alone several.
I hope some of the selections I suggested for you were to your liking. Will any be useful?