This is a very complicated topic and it depends mostly if your HSA is individual or group insurance from your employer. If you have a group coverage it does not really matter if you are HSA or not from the standpoint of getting the group insurance. By federal law as long as you have been covered by group insurance you cannot be denied by your next employer's insurance group coverage, and you will be fully covered at your employer's rates. The HSA option may not even be available with your next employee

If you are looking at individual coverage, it is regulated by the state you live in so basically anything can happen.The state may sponsor your insurance, or refuse to sponsor, or force you into HSA, or prohibit forcing you to HSA. Check with your state insurance commission for guidance. HSA is quite an uncharted territory.

On a personal note, HSA may be a good deal from a tax standpoint, but if you incur a lot of expences and switch jobs and  you may lose a lot of money that year. That is because your deductible will reset, but tax deduction for the HSA contribution will be pro-rated. For example mu son had surgery, so I had used all the deductible (5000) in May. I switched jobs in June so I had to pay a new deductible for the rest of the year. To add insult to the injury the Feds allowed me deduct only 2500b because the deduction maximum is pro-rated on monthly basis.