All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The narrations about starting with the right side (before the left side) in every act are authentic and there is no doubt about them. Rather, some of these narrations are among the most authentic narrations as they were agreed upon by Al-Bukhari and Muslim like the narration which is narrated by 'Aa'ishah who said: “The Prophet used to prefer to start with the right side (over the left) when putting on his slippers, combing his hair, ritual purification, and in all his matters.”
Therefore, what you do by starting with the right before the left is not an innovation; rather it is a desirable Sunnah for which you will be rewarded, Allaah willing. Hence, we encourage you to do this Sunnah and continue to spread it and invite people to do it, and teach the children and elders to do it, and you will get the reward of whoever does it without diminishing anything from their reward.
For more benefit, please refer to Fataawa 88498 and 84990.
Allaah Knows best.