I have a family member, a cousin to be more specific, who is in one of the thousands of protestant sects that combines judaism with their form of "christianity." She lives thousands of miles away from me so we can only exchange e-mails and information online. Anyway, she's in the type of sect where they celebrate jewish feast days, for example.
If your cousin is in a twisted, tyrannical cult she should get out for that reason alone.
Assuming that is not the case and we are merely dealing with an eccentric form of Christianity, my remarks are:
You have not told us enough about your cousin's beliefs and practices for us to be able to come to any firm conclusions. You say that they "celebrate Jewish feast days." But what days do they celebrate, and how do they celebrate them?
•I see nothing wrong in principle with reciting the 19th (18th by your count) Psalm on Saturdays and saying a prayer of thanks to God for creation and the Sabbath.
•I see nothing wrong in principle with assembling on Saturday for Bible study, as long as the Sunday assembly is not neglected.
•I see nothing wrong in principle with giving thanks for the evening lamp on Friday night or any other night.
•I see nothing wrong in principle with giving thanks to God after
eating, as well as, or instead of, before eating.
•I see nothing wrong in principle with pronouncing a blessing on viewing striking meteorological or astronomical phenomena. Ben Sirá writes:
Look upon the rainbow, and praise him who made it, exceedingly beautiful in its brightness.
So if Irish children, on seeing the new waxing moon, can sing
I see the moon,
the moon sees me,
God bless the moon
and God bless me.
There's grace in the cottage,
there's grace in the hall,
for the grace of God is over us all.
then I don't see why your cousin can't greet the new waxing moon saying
Which can be transliterated in Roman characters
and means something like
Blessed is your Shaper,
Blessed is your Maker,
Blessed is your Owner,
Blessed is your Creator.
•I see nothing wrong in principle with celebrating a Fall harvest-festival (Sukkoth) by setting up an awning outdoors and having dinner under the awning.
•I see nothing wrong in principle with lighting candles at midwinter in honor of the Maccabees.
•I see nothing wrong in principle with adopting a spiritual discipline of not eating swine's flesh, any more than I see anything wrong with the spiritual discipline of not eating the flesh of warm-blooded animals on Wednesdays or Fridays.
Spiritual disciplines can be helpful or hurtful depending on how implemented. So you need to give us some detail about how your cousin's society implements the practices you refer to.