You want your audiences to respect you? Of course. You strongly disagree with the attitudes of some individuals in your audience? Of course - it happens to all speakers, at presentations and just speaking up at meetings.
But do those attitudes make you feel 'unsafe'?
Here's the bad news.
You cannot feel 'unsafe' and have personal authority at the same time.
You're serious about speaking with personal authority? Then make every effort to abandon the damaging psychological condition of I feel unsafe when confronted with disagreeable words and ideas. The condition will seriously limit your ability to make your own ideas heard. In fact it is doubly dangerous.
How ironic that the real danger is not in being unsafe, but in adopting the 'I feel unsafe' mentality. And yet no one can make you feel like a victim without your permission.
Am I overdoing how you interpret the word 'unsafe'? Unsafe means that you feel threatened - the original meaning implies physical danger. But maybe those disagreeable attitudes just make you feel uncomfortable and you've adopted the word 'unsafe' to describe it. But either way - unsafe or just uncomfortable - you're not doing yourself any favours by allowing that state-of-mind. Instead...
Choose to be comfortable with the natural diversity of ideas and beliefs in your audience.
Choose to be comfortable when a member of your audience expresses ideas utterly opposed to your own. Those ideas are an inevitable outcome of that person's background. You are above feeling threatened. You are a leader.
That does not mean you should ignore such individuals, or write them off as just 'politically correct', or reply with dismissive aggression.
It does mean this...
Respond passionately and respectfully with your own opinion. Verbally disagree with the individual with a manner and body language that accepts the person. That person gets the same warmth as anyone else. No to the ideas, yes to the person - simultaneously. It takes the steam out of them.