What to do if one out of 2 one-hot encoding variables have a very high p-value?
You should keep all of levels as they collectively describe the feature. Removing the insignificant ones will bias your coefficients and distort your interpretation (e.i. change the reference level).  

Here are some stats.exchange references:


Is it advisable to drop certain levels of a categorical variable?
Can I ignore coefficients for non-significant levels of factors in a linear model?