There is a (very widely held, to be fair) misconception that DBS checks ought to be done in all sorts of circumstances as a reassurance, when actually access to them is specifically restricted to occupations and situations where it's relevant to have one. Anyone can have a basic check, but enhanced and even standard checks are specifically limited and ring-fenced and this would not be the type of situation where they would be available. Also, they are only really current at the point you get them, and are no guarantee whatsoever that in the 18+ years between donating and potentially having contact with adults born as a result of that donation, the donor won't commit all manner of crimes. I'm not saying I think that's particularly likely, but you take my point.
Requiring DBS for donors would also place a higher burden on the donor than on the actual parents having the child, where the Welfare Of The Child process only asks about very specific convictions regarding crimes against children. This doesn't seem proportionate given the donor won't have any contact or involvement at all during the childhood of anyone born as a result of their donation, and may never have any once they reach adulthood.
I think perhaps what the OP is reacting to here is not so much risk, as a fear that a donor's values may not align with their own. That's a very valid thing to be thinking about in relation to donor conception, and the OP has definitely come up against it in a particularly dramatic way which will have been very unsettling and upsetting, but it's there for everyone on some level. It is possible that 18+ years down the line we might find that our child's donor is someone we think is awful (or, indeed, someone who thinks we are awful). And ultimately I'm not sure you can completely mitigate against that.
I'm pretty sure that one of my son's donors was at some of the same protest marches as me, for instance, from the information they provided. And that's a nice feeling to think we might be somewhat similar, but there's no guarantee that they won't change over time and by the time my child turns 18, they might have changed. Or I might. Or my child might disagree with both of us! (And of course it could happen that people diverge just as easily in a relationship. One only has to look at Billie Piper's situation to see how difficult that can be). There are views a person could hold, for example, that yes, I would find challenging (if they were a raging racist, for instance), but ultimately I'm not able to control that and it falls into the category of things I'd have to work through, and help my child work through, if their donor turns out to be someone very different to what we might have hoped or pictured. I do think counselling is a helpful forum for that.
And I agree with@blueandgreenandyellow in suggesting that a broader framing, I think that would be really productive.
Best of luck, OP, whatever your journey brings.