Someone with an undetectable viral load is "positive" - they carry antibodies for HIV, and although HIV is undetectable in their blood, where their HIV drugs circulate and are most effective, the virus remains hidden in other tissues. Yes, you can still get HIV from contact with an undetectable partner, although the risk is less than 1/20th the risk otherwise, low enough that it's difficult to study. See this recent study, of mixed-status couples. These were people under intensive testing and care, of course. The greatest risk is probably that undetectable people can quite quickly become detectable again, with any irregularity or failure in their drug regime or change in their virus, and neither they nor their partners will know this until they're again evaluated. For the highest-risk sort of contact, particularly with anyone other than a live-in partner whose health and status you are always aware of, it would be best to observe the usual precautions. I was in a mixed-status relationship for years, and yea, the usual precautions are a bit of a chore, but do become a routine. Outside a relationship, it's something to negotiate, but if you are not comfortable asserting yourself or your partner presses you to risk your health, even a little, move on. You deserve better.
This is no longer considered true. 10 years of studies with thousands and thousands of serodiscordant couples (one poz, one neg, the poz man undetectable) has resulted in zero transmission. Condoms fail 2-8 percent of the time. The scientific consensus is endorsed by almost everyone including the CDC. The greatest risk still remains from men or women who don't test and assume their status is negative, by a massive margin. Everyone must choose for themselves what they think is risky and what is not, but the strategy most have used which is turning down Poz folx who disclose has had awful repercussions, both in terms of stigma but also the ongoing crisis, because a person is only as negative as their last test before sex again.