Answer:
There is no problem in the marriage between Sayed girls or women with non-Sayed Shiite men as it is not necessary for Sayed girls and women to marry Sayed men [1] . None of the jurists have forbidden such a marriage.
For instance, Grand Ayatollah Saafi Gulpaigani says in this regard as such:
“No, there is no problem in it but it is befitting for the husband to further observe his wife’s respect.” [2]
Imam Musa Kazim (a.s.) had many daughters who did not marry throughout their lives like Hazrat Ma’suma but it was not because of the unavailability of Sayed men.
[1] - Hawzah Net (website): “marriage between Sayed women and non-Sayed Shiite men.”
[2] - http://www.saafi.net/node/2894