Can I take part in a lecture series on Kaballa (introduction on ideas) and other Jewish topics when the instructors aren’t religious and even living with a Goya?

Generally, the answer is clearly no. Not any Jewish studies and how much more so Kabbalah. Though, in some extreme cases a rabbi that knows the individuals involved should be consulted, since not all cases, places or times are the same. It can depend on who the teacher his and what his personal background is, what exactly and how he teaches, who the student is, what are the alternatives available, is there any additional influence on the student, what is the impact on the wider community etc.