Rigidly is often used to describe something that is very stiff or inflexible. However, there are many other words that can be used to convey a similar meaning. Some good synonyms for rigidly include firmly, tightly, securely, unyieldingly, inflexibly, stiffly, strictly, and closely. Each of these words can be used to describe something that is very stable and won't easily move or change. They can also be used to describe someone who is very set in their ways or who refuses to budge from their opinion. By using these synonyms, you can add depth and variety to your writing while still conveying the same basic meaning.