Here is the verse from Ramayana that Rama left eating meat for 14 years.
चतुर्दश हि वर्षाणि वत्स्यामि विजने वने |
मधु मूल फलैः जीवन् हित्वा मुनिवद् आमिषम् || २-२०-२९
I shall live in a solitary forest like a sage for fourteen years, leaving off meat and living with roots, fruits and honey.
Lord Rama Chandra, even being a king, stood on his oath and left eating non-vegetarian food for 14 years.
So I think, today's Hindus should learn from it to avoid eating meat as there is no more a system of a king ruling a kingdom. Exception should be only for a few like soldiers, sports persons and laborers etc.
In Sundarakanda, Hanuma is telling Sita and she is listening with a lot of happiness filled in her eyes. I am writing here with utmost respect towards Rama Chandra prabhu. Hanuma is telling about, then current condition of Rama as:
न मांसं राघवो भुङ्क्ते न चापि मधुसेवते |
वन्यं सुविहितं नित्यं भक्तमश्नाति पञ्चमम् || ५-३६-४१
Meaning: He is not eating meat anymore, nor indulging in liquor (not even spiritual liquor) and he is just eating the fruits available from forest which are well arranged for him.
īśāvāsyam idam sarvaṁ
yat kiñca jagatyāṁ jagat
tena tyaktena bhuñjīthā
mā gṛdhaḥ kasya svid dhanam
Everything animate or inanimate that is within the universe is controlled and owned by the Lord. One should therefore accept only those things necessary for himself, which are set aside as his quota, and one should not accept other things, knowing well to whom they belong.
Kings are allowed to eat meat. Lord Rama ate Deer meat. Sita cooked it as per Ramayana. Sage Agasthya ate meat during a ritual where Pitru Karma is performed. During Pitru Karma or performing rituals of the dead, eating meat was allowed in olden days but not in kaliyuga. That's why when sage Agasthya ate meat he digested Vatapi with his saying "Jeernam Jeernam Vatapi Jeernam". Likewise Dharma varies based on the time and period. It has to be taken wisely to eat meat or not. So it depends on time and period and based on one's conscience. Nowadays it is very tough for people to give proper Dharma on eating meat in this Kaliyuga. But it is very much advisable to avoid it.