There are many authentic hadeeths from the Prophet ﷺ saying,
“Whoever has eaten garlic or onions should not approach our mosques.”
(Bukhaary 855 and Muslim 564),
and, in some narrations, such a person has been ordered to leave the mosque. (Muslim 567) In any case, if a person must eat garlic or onion then he should not cause harm to others due to its smell, or he should not eat it at the times of prayer so that it does not cause him to miss out prayer at the mosque and in congregation. Once people heard that the Prophet ﷺ prohibited anyone who ate garlic to come to the mosque, some companions proclaimed that eating garlic was prohibited! Once this reached the Prophet, ﷺ he said,
“People! It is not for me to make prohibited what Allaah has made permissible, but it is a vegetable whose smell I detest.’ (Muslim 565)
Hence, if the vegetables are consumed for medicinal purposes, there is no fault in eating them. However, one should try to eat them at times which will allow the smell to vanish before prayer times starts. If there remains a light smell of it and fragrance can mask its smell, that is acceptable, since people will then not find its smell offensive. This is how simple it is. Now to the question regarding someone who has eaten garlic or onion and his neighbor struggles to tolerate it. In such a case if a person can somehow complete his prayer, then he should do so. If he cannot tolerate it, because people have different tolerance levels and some can bear it and some cannot, there is no harm to stop the prayer and to move to another place. Thus, it becomes clear the wisdom behind why the Prophet ﷺ told people who have eaten garlic and onions to stay away, because it can cause others offence. There are those who cannot tolerate it, there are those who can, and there are those who are sensitive to the smell. In any case, a person must reduce this as much as possible and if eaten, it should be at times which would allow the smell to disappear before prayer times start. The same applies to those who smoke or do not take care of dental hygiene. In short, anything which causes offence to someone else should be stopped.
(وَٱلَّذِينَ يُؤۡذُونَ ٱلۡمُؤۡمِنِينَ وَٱلۡمُؤۡمِنَٰتِ بِغَيۡرِ مَا ٱكۡتَسَبُواْ فَقَدِ ٱحۡتَمَلُواْ بُهۡتَٰنٗا وَإِثۡمٗا مُّبِينٗا)
“… and those who harm believing men and believing women for something other than what they have earned have certainly borne upon themselves a slander and manifest sin.
(Al-Ahzaab 58)
It is similar for a person leaving his cell phone on loud and the ring tone plays music while people are trying to pray. This, without doubt, causes people to be upset. It would be unfortunate that such a person should fall under the warning mentioned in the aayah.