If I have one non-significant factor level in a glm, is that entire variable now considered non significant? I have a question similar to this one, but I just wanted to follow on and ask if the entire variable is now insignificant? I have a factor with 3 levels. When doing the model simplification, it showed that two of the levels were significant, and one was not (p = 0.5). Can I still consider the other two levels to have a significant effect on my response variable, or is that entire variable now non significant? (I expect the insignificant level was insignificant since the sample size for that level was only about 3) Thank you!

When you have a factor variable in a regression model, that is, a categorical variable with multiple levels, that variable should be treated as a whole. So you should mostly disregard the t-tests for each separate level, and test the variable as a whole. In a linear regression model that would be an F-test. Such multiple-df tests are often called chunk tests, see What are chunk tests?.
Most of these is explained in the post you linked. The post I linked above contains examples.
As pointed out in a comment by user Frank Harrell, one specific reason to ignore the 1-df tests is tat they depend on the categorical encoding used. That is, they test specific contrasts, which might well be without any interest to you, especially if you only used some default coding.  See my answer at categorical independent variable with three levels and binary logistic regression
