Taylor,
This would depend on the terms of the shares after the SAFE converts into equity. This is Company specific.
I assume your question applies to a Company that is not public, and the SAFE converts into equity in a private investment round (Series Seed, Series A, etc.). In that case, the most common scenario (if you are using standard NVCA documents) is that investors are not allowed to transfer to a competitor, but otherwise can transfer their shares so long as the transfer does not create an issue under the securities laws. Some companies will go further and require that some or all investors are subject to a right of first refusal and/ or co-sale right, where the Company and the other investors or shareholders have the right to purchase the shares in the proposed transaction, and possible to co-sell /tag along in that same transaction. Even further, some companies will also include outright restrictions on transfer unless approved by the Board or some major stockholders, although I would say this is rare in the tech market.
If the Company is public, then there may be investor lockups, black out restrictions and all sorts of limitations on the right to sell. That is a much more complicated situation, and again is Company. Hopefully, that is not applicable in your case.
Dimitry Herman