Is it an SEO problem if I change an SSL certificate from that of a large web hosting company to one that is free software?

I noted in a thread a couple of years ago that people can, if they're curious, tell about how much you paid for your certificates (and for that matter other aspects of your web site technology), and they could choose to make judgments based on that. They might be more impressed if they see that you spent more money on the site, even if you didn't have to.

There isn't necessarily a way to predict this. Other people could also think negatively of you if they saw that you spent more money than you had to.

I think there are cases where seeing that someone spent resources on something builds credibility, and web site infrastructure is less and less often one of those cases.