I'm planning to do that, however I am just wondering whether the HELOC on property A (debt-free primary home in my case) will negatively impact my ability to get cash-out refi on B (an investment)?

An HOA may allow them today and then ban them completely next week.

., for example, are outright banning short-term rentals or enacting strict rules such as requiring that owners live on the property for a period of at least 6 months each year.

Then the practice was banned.

If you are thinking of going this route, make sure you check both any HOA rules and local municipalities limitations or outright banning of short term rentals before you decide to buy in that area. 

They can ban rentals easily.

I talked to a STR manager though the other day, and he was talking about all the rules in place and I was thinking about the idea of banning investors owning homes.

On the one hand, eviction bans left many stuck with nonpaying tenants, and bills just piling up.

Costar has very strict rules on sharing and they will ban the account.

Las Vegas has banned STR's from what I understand.