Question: There are those that kiss their Tzitzis during Shema at Shacharis as per Kitzur Shulchan Aruch 17:7 and the Kaf HaChaim 18 and there are those that do not. What is the source and reason for those that do not kiss their Tzitzis during Shema at Shacharis?

Answer: 
I have not the exact halachic sources but read that some poskim considered those kissings during the shema as hefsek, for example : The Vilna Gaon, Chazon Ish, The Steipler, Rav Moshe Feinstein (read there : <https://halachafortodaycom.blogspot.com/2012/04/q-page-1.html>)

Also I read once that some don't even grasp their tzitzios during shema like for example Rav Chaim Soloveitchik but that's an other subject.
The Bet Yosef says (paraphrase, see comments) 'some say it is pride to kiss the Tzitzis while praying Shema. And some say there is no pride because it is a very common practice. And the second one is the Minhag.' I guess some people are still Hoshesh to the Isur of Yuhura.