My DH was a SAHD when it was even more of an unusual set up. I can honestly say the only person who was negative was my paternal grandmother who came from an era and background where this would have very unusual!
If your DS was very little when you started, bear in mind that a lot of mothers meeting up in the first few months are still talking about birth and post partum physical issues - they may not care to have a man involved in these conversations. My DH was always careful to bear this in mind.
It took a bit of time for people to start inviting him to stuff (this suited him as he is an introvert) and he found that he made friends with people very similar to him - so no different from friendships in every day life. As our DC got older we did notice some people were reluctant for their DC to come to sleepovers if there was only a dad present, which was a bit insulting to DH.
On the whole though, he was recognised as a brilliant parent, he enjoyed it very much and DC bridge a lot of gaps. The pinnacle of his SAHD days was when he was asked advice on breastfeeding 
Agree, do not say "full time parent" and be respectful that there are areas of becoming a parent that are specific to mothers/women. Otherwise treat situations as you would in any social gathering.
I actually seemed to get more annoying comments than DH did, it was almost as though I had some exotic pet which was doing me a favour. I strongly believe we will only advance equality for women when men really properly share responsibility for childcare and domestic duties.