They want you to have lessons with their priest, be baptized by them, and only receive Communion there.
It depends on who you are as well. At least one of the priests is a little lenient on the rules for some.
If you've been to a Thuc line priest, believe that some or all of the Thuc line is valid, you may not go to Communion. Adults have to sign statements against them, I don't know if children are required. I think some of this is in their bulletin. Also, I know that it is an unwritten rule that one cannot go to mass at to an SSPX ordained priest who believes the Thuc line is valid. He cannot associate with them, either.
They also frown on friendships with people who go to "Thuc priests." Those that I know who go there are terrified of losing the sacraments and will do anything to keep them. Personally, I think it is a control issue. I don't hesitate to call them a cult.
By the way, Bishop Kelly has been noticeably absent and mysterious these days. No one that I know of has had direct interaction with him. That seems really odd.
Someone like me who goes to CMRI, according to the SSPV, is equal to a non-catholic, no sacraments and I can't be a sponsor for baptisms or confirmations.
I'm not so sure that people who go to SSPV where they are further away from CMRI or independent chapels know about this. Someone invited me to an SSPV retreat a few years ago and I had to explain to her why I couldn't go. I think she might have checked up with them as I never heard back from her again.
Anyways, I'm open to correction if I have misstated anything, but as far as I know this is all current and true.