THdividing issue between CMRI and SGG on the one hand and SSPV on the other is the Thuc Bishops. The SSPV regards the ordinations performed by Abp. THuc as doubtful. Therefore it is a sin to participate in sacraments that can be shown to be objectively doubtful.
SGG and CMRI on the Other hand have Thuc line Bishops (Bishop Pivarunas in CMRI, Bishop DOlan at SGG and Bp. Sanborn Affiliated with SGG). Fr. Cekada has done a wonderful job on
http://www.traditionalmass.com in demonstrating the validity of the Thuc line Bishops.
The SSPV however believe he is deluded. THere is still controversy, though in MY OPinoin, Fr. Ckada has settled the matter. The Thuc Bishops are a valid line of succession. The SSPV generally misapplies canon law and Papal Encyclicals to Abp. Thuc to make excommuniate. Fr. Cekada demonstrates that these do not apply, and therefore exonerate him.
Consequently the SSPV will not commune anyone from CMRI or SGG. Although I believe CMRI and SGG will commune those from SSPV.
Also, CMRI and SGG take a more dogmatic approach to the issue of Sedevacantism: For them it is an article of faith. For the SSPV it is a porbable opinion.