Answer to: "Is there harm in starting the month of fasting while junub?" is: NO.
Issue: Among the benefits of allowing sexual activity, eating and drinking until dawn for those who are fasting, is that it is allowed to start the fast while Junub (in the state of impurity after sexual discharge), and there is no harm in this case if one takes a bath any time in the morning after waking up, and completes the fast. This is the opinion of the Four Imams and the majority of the scholars. Al-Bukhari and Muslim recorded that `A'ishah and Umm Salamah said that Allah's Messenger used to wake up while Junub from sexual intercourse, not wet dreams, and he would take a bath and fast. Umm Salamah added that he would not break his fast or make up for that day.
Muslim recorded that `A'ishah said that a man asked:
يَا رَسُولَ اللهِ، تُدْرِكُنِي الصَّلَاةُ وَأَنَا جَنُبٌ فَأَصُومُ؟ فَقَالَ رَسُولُ اللهِصلى الله عليه وسلّم:
«وَأَنَا تُدْرِكُنِي الصَّلاةُ وَأَنَا جُنُبٌ فَأَصُوم»
"O Messenger of Allah! The (Dawn) prayer time starts while I am Junub, should I fast'' Allah's Messenger replied, (And I. The prayer time starts while I am Junub and I fast.)
He said, "You are not like us, O Messenger of Allah! Allah has forgiven your previous and latter sins.'' Allah's Messenger said:
«وَاللهِ إِنَّي لَأَرْجُو أَنْ أَكُونَ أَخْشَاكُمْ للهِ وَأَعْلَمَكُمْ بِمَا أَتَّقِي»
(By Allah! I hope that I have the most fear from Allah among you and the best knowledge of what Taqwa is.)
And Allah Knows Best