What? Really? Why not?
The SSPX understands itself to be a congregation of common life without vows. That means that it belongs to the style of religious institute that lives in community under superiors whilst still retaining the status of secular clergy (diocesan priests are secular clergy). They have
de facto poverty rather than vowed poverty, a promise of celibacy rather than vow of chastity, a promise of obedience rather than promise.
Putting aside the moral arguments against social media -- these are strong arguments, in the view of the SSPX superiors, the possession of social media accounts by individual priests members would do nothing to promote the sanctity of the priest, would distract the priest from his sacerdotal and community vocations, could misrepresent the positions of the SSPX. Therefore, whilst the SSPX has corporate social media accounts administered by the communications offices of the congregation, individual priests of the SSPX are obliged not to have such accounts.
In the days long before social media or even the ubiquitous use of cell phones, we who were STAS seminarians did not have PCs, TVs, stereos, or private telephone lines. I had a crappy, plastic knock-off Walkman on which I played audio cassettes from Keep the Faith kept in a box in the common room or had been sent to me by chapel friends from back home.