A young Sunni widow is not remarrying because of widow remarriage being a taboo in her society but is willing for Mutah with a married Shia acquaintance. Is that allowed?
Bismihi ta'ala
If you are asking if it is jurisprudentially allowed, then the simple answer is yes, if she was to perform temporary marriage with a Shi'a male it would be valid.
However, is it socially advisable for her to do so. I would encourage her to think for the future and focus on long term relationship, settling down and marrying someone. This would be better for her on many levels.
Her getting involved in mut'ah, and not knowing how long it will last, and whether the man will respect her reputation, etc, will be more socially damaging for her.
As for the taboo of remarriage, this is something we must all fight against, and reclaim what our religion favours for us as a society.
With prayers for your success.