I'm surprised to hear that. Seems like I am ignorant of the true liberalism of the SSPX.

As a general answer I would say yes, although it can vary widely depending on location and the mindsets of the individual priests.

In my experience, SSPX anti-homeschooling sentiment is most likely to be found in the larger communities with well-established schools (think St. Mary's, Post Falls, etc. ). As Matthew said, in the SSPX mindset homeschooling represents competition to the school, and in these places the "competition" is very direct. Therefore, unfair bias against those who choose to homeschool can be very pronounced in these locations.

Most folks in these communities who homeschool appear to do so for the right intentions (they disagree with liberal elements or they are trying to escape other obviously serious problems with the schools). Strangely enough though, there is also often a minority who homeschool in these communities for the "wrong" reasons (don't want to dress modestly, indult-minded, took issue with the outspoken priest who criticized Pope Francis, etc.). Obviously, these examples of poor formation often have poor outcomes because they are inherently liberal-minded. Unfortunately, the leaders/teachers of the schools cherry-pick these examples of poor formation, and then smear homeschooling as a whole. They then make joining their school a sort of spiritual crusade, while at the same time not properly addressing the spiritual and physical problems in their own systems.   

On the other hand, in SSPX mission chapels it can vary widely depending on the individual priest. Many seem to "tolerate" homeschooling if there is no other practical option. However, I have also seen some who encourage families in this regard by having "homeschool days" to share materials. Most of the ones who seem favorable to homeschooling are the older "hard-liner" conservative SSPX priests rather than the youngest ones. Not sure what their "theoretical" thinking is about school vs homeschool in an ideal world, but they don't seem antagonistic to homeschoolers in the practical context.

It's simple.

Homeschooling is better for the child, in most cases. But sending your kid(s) to the SSPX school -- assuming there is one -- is better for the SSPX organization.

Guess which "good" the SSPX priests focus on? You guess it -- the good of the SSPX.

The SSPX would rather have 1 new Trad attending one of their chapels -- and putting donations in the collection every week -- than 10 new Trads attending a "competitor".
Sad? Shocking? Unbelievable? But I must say, in my experience it's unfortunately true. Maybe a few priests are more selfless, remembering that it's about God and the good of souls. But for so many neo-SSPX priests, they don't care what's better for souls, even specific souls. They care FIRST and FOREMOST about the good of their chapel, their organization.

The proof is the whole new orientation. No one can say a sellout is good for souls, the Church, the cause of Tradition, etc.! But it's better for the SSPX organization. And so...

They have adopted a completely worldly, materialist mentality. They are obsessed with image/brand, (hence their hiring a corporate branding firm), numbers, their reputation among infidels and Conciliar Catholics, and other human concerns.

McDonalds would rather have 1 new customer, than see Burger King get 10 new customers. That's fine for a restaurant. There is no "good for souls" in eating fast food. But Trad chapels should be happy that souls are being taken care of, WHEREVER they attend the Tridentine Mass. The priests should be glad to have help, even if that help is from another "rival" organization.

Do you think St. Isaac Jogues and the other North American Martyrs (read their adventures sometime! Quite edifying.) would have been so territorial? Or would they be happy to have any help they could get? They labored constantly to convert souls to Christ, while simultaneously fighting against the devil and his minions in the world, who constantly work against the salvation of souls. See, the saints had a SPIRITUAL, SUPERNATURAL mindset. They understood that the world was a huge battle God vs. the devil, and they kept that big picture in mind always. They weren't concerned with credit, numbers, earthly glory, real estate, or any of that.

It's simple.

Homeschooling is better for the child, in most cases.