A lot of people look through celebrities or public people's tweets and likes because they are interested in knowing more about them. It's like when people invite cameras into their personal life and people start following them on social media and want to know more about them and they grow a fandom. I think what happened with Courtney is that some skating fans were looking at likes to various skaters and then came across hers and then saw a few things they didn't like. Or maybe they saw something she re-tweeted that showed up on their feed and looked at her likes to see if she expressed support for other views like that just to be sure before they made a judgment. Then they told their friends, and then they told others, and then some reacted in a way where they became more openly hostile and confrontational about it.
As for your other question about her retweeting or liking any homophobic things, I just checked yesterday when this whole conversation was going on and I saw she liked something pretty transphobic and also tone deaf of the experiences of black people:
https://twitter.com/SyrOrangeJC/status/924028266796670977
Courtney actually liked some of the more negative comments. The last reply in the above thread where the person hashtagged #girlbye to Hicks was liked by Hicks. So she's pretty proud.
Anyway, I think Hicks is young and discovering her political voice and is enthusiastic about others whose views she shares. I think the ones responding to her are similar in age and also discovering their voices. So you have young people yelling at each other. This is pretty much how the 2016 election discourse was happening on social media except it wasn't just young people and some times people were positively reacting to bots.