Some remarks:
1) The news is true. In an internal email, the District Superior stated, "Today our beloved Society has officially become the owner of one of the most prestigious and beautiful churches in Vienna, the Minorite Church of Madonna della Neve, in a prime location in the 1st district right next to the Federal Chancellery."
2) The Minorite Church (Friars Minor Conventual Church) is actually privately owned and does not belong to the Diocese. This is for historical reasons (expropriation of church property under liberal/masonic Emperor Joseph II. and subsequent donation of the church to a private association, the Italian Congregation).
This private association has now transferred the church to the SSPX. Why, I do not know. In the comments at “gloria.tv” there are two pieces of information:
a) the Italian Congregation did not want to give the church to the diocese under any circuмstances
b) the church was supposedly offered to the Society of St. Peter before, but the latter did not react (probably to avoid a conflict with the diocese).
3) The SSPX has had a branch in Vienna since 1981. Since 1984 the SSPX has celebrated Mass in the present chapel. However, for almost 20 years they have been looking for a better location. In this respect, the interest in vacant or empty churches is not surprising.
4) Why the church was finally given to the SSPX, I cannot answer. However, one should not forget: Maintaining such a huge building and all the artwork is very expensive. It happens again and again that in Austria you can buy an old building for a symbolic Euro, but with the obligation to maintain this building. And this is where the financial challenge lies.
5) There is certainly no connection with the SSPX position on vaccination. This is a completely unfounded and arbitrary speculation.
My personal assessment
The matter is not yet settled. There will certainly be attempts to challenge the donation.
I would be happy if the SSPX does not get the church. The financial burden would be gigantic.
Above all, the SSPX would be in the spotlight. This is not a small village church but one of the most important churches in Vienna, absolutely in the center, right next to the Chancellor's official residence. There is also a lot of tourism there. In addition, Cardinal Schönborn's anger will ensure that what is done or said there is closely monitored. Easily scandals can be produced and maybe even violations of the law (e.g. hate speech) can become a huge problem for the SSPX.
The pastoral care is not helped by all this. (At the time of the persecution of Christians, Christians also did not erect a religious building on the Roman Forum. It is no different today. The superiors should be a little more wise about this).