Is it possible to assign taxonomy to posts at the same time?

Yes! You can do it in WPBULKiT – Bulk Edit WordPress Posts / Pages Plugin through 2 ways:

Inline Edit/ Bind Edit

1. Select your posts
2. Checked the “Bind Edit” if you want to edit multiple posts at the same time
3. Click on the “Taxonomies” field such as Category, Tags or Custom Taxonomies
4. Select desired terms for each taxonomy

Bulk Edit

1. Select your posts
2. Checked the “Bulk Edit”
3. Select your desired terms for desired fields in the ”Categories/Tags/Taxonomies” tab
4. Click on “Do Bulk Edit”

The above operation is fully stated in the separate article, which you can read if necessary.

Read More: How to bulk edit post/custom post custom taxonomy in WPBULKiT – Bulk Edit WordPress Posts / Pages Plugin?