I’m not too eager to insert myself into more TLM/NO squabbling, and I know this is not the same thing as the TLM/NO debate, but may I offer my own experiences from attending an Anglican Use (AU) parish so as to offer a possibility as to how the TLM worshippers, only, crowd, and the NO worshippers, only, crowd can intermingle under the same roof?
After all, a principle in canon law is that when no law exists for a particular situation, recourse is made to parallel passages in law. So let’s borrow a principle from the canonists, shall we, to see if we can’t have similar experiences?
At my church, we have a 7:30 am, 9 am, and 11 am Masses said in the AU form. At 6 pm, we have Mass said in Latin according to the Ordinary Form (OF) of the Roman Church (yes, it is the exact same Mass said in most other Roman Catholic Churches across the globe). Now, for the chief solemnities of the Latin Church, Mass is sung according to the AU Form, but the Schola Cantorum from the OF Mass gets to sing, in Latin, on these occasions. In addition, we have Solemn Choral Evensong (as opposed to Latin Vespers) sung according to the AU Form on the occasion of the Solemnity of All Souls, but the Schola Cantorum gets their say, or rather their sing, at the Evensong. That being said, during Advent, the Schola gets to sing Latin Compline. In this way, all the people of parish get to experience the richness of the Latin Church. And needless to say, all the worshippers share the same parish gatherings, scripture study (there is only 1 Gospel, right?), etc. Speaking for myself, while I sing for the 11 am Mass, I occasionally go to the 6 pm one as well.
While I have never been to a TLM Mass in person, I’ve seen video clips of it, and appreciate the beauty of it. Therefore, in short, yes, I think it is possible for TLMers and NOers to intermingle in the same parish, and I humbly offer my own experience at an AU parish as a parallel to how such a TLM/NO parish might be like.
Issues like female ordination and other forms of heresy should not be in ANY parish which believes that Pope Benedict XVI is true Vicar of our Lord Jesus Christ, so if you have that in your church, you have have even more serious problems to deal with—these are not intrinsic to the NO parishes, nor, am I completely (I have a gut feeling on this, no proof, but just a gut feeling) convinced that the TLMers are fully absent of them.
Remember that the external form of worship (as long as it is approved by the competent authorities, namely the Holy Father himself for us Latins, and is done reverently) is not the substance of the Faith, but rather an expression of it. The substance of the Faith, as regards the Eucharist, is that bread and wine truly becomes for us the Body and Blood, Soul and Divinity of our savior Jesus Christ, who is true God and true Man, that a priest alone offers it on behalf of his fellow worshippers (“Take this…do this in memory of Me”), that all worshippers are commanded to receive it sometime by divine law (“Unless you eat…”, “If anyone shall eat of this bread…unworthily, he shall be guilty of profaning the body…”), and Christ Jesus is truly raised from the dead (bodily and spiritually, not like a ghost, or to the other extreme, like a zombie), otherwise all of this would be in vain (St. Paul: “If Christ is not raised from the dead, you are still in your sins” and consequently, the Mass could not remit them.) .
It is important for all Catholics to see a variety of legitimate and reverent expressions of the Faith, for then we see that the command was universally (as opposed to regionally) given to the Church to baptize all nations
In nomine Patris et Filii + et Spiritus Sancti, teaching all that was commanded.