Can having oral sex with someone who has a canker sore cause problems?

Protect yourself!: Exposing yourself to a possible infectious agent from an open wound is never a good idea! if your partner's "canker sore" turns out to be a herpes lesion, you run the risk of getting a herpes (type 2) infection on your private parts. Such a herpes infection become potentially a lifelong relapsing & painful problem that you can then pass on to others--not a good tradeoff for an impulsive moment.

Yes: Depending on the type of sore, and whether or not you have already been exposed to the same virus in the past, you could pick up the infection. Once you do, it's yours for life.

Yes: Especially if that canker sore happens to be herpetic (cold sore). Don't do it!