Pending further comments from the SSPX Headquarters, let us quote the official SSPX news agency FSSPX.NEWS, which stated on June 3, 2021:
"We can only reaffirm what that such a restriction on the Motu Proprio of Benedict XVI, would be perfectly “abusive,” and since it would be directed against the common good of the Church, it would be “null in itself.” Although the Society of Saint Pius X may not feel concerned, “it would deeply regret such a limitation, because it would be a step back on the way back to Tradition which would delay the solution of the crisis of the Church.”
However, this new persecution against the Traditional Mass gives us proof that Archbishop Lefebvre was right when he said that the Old Mass cannot coexist with the New Mass. The New Mass was made to replace the Old Mass and what it carries, that is to say the two-thousand years of Tradition of the Church. It was replaced by a completely New Mass which express a new faith, which is not Catholic: "lex orandi, lex credendi".