Ben Shapiro vs Neil deGrasse Tyson: The WAR Over Transgender Issues

[Sheldon]

Yes, the earth is not flat, is not just a subjective opinion, as it rests on an amount of objectively verifiable evidence, that would make denial of it unreasonable. I tend to think of objectivity as a scale, the more objective the evidence, and the more objective evidence we have the more reliable the conclusions it supports. 

Excellent.  It's those types of assertions which metaethical objectivists would refer to as "valid" moral assertions.  They accurately report the thing they purport to report.  

Great give me an example of a moral assertion that doesn't rest on a subjective opinion and we're done. 

It's an objectivist moral assertion because it purports to report a fact of the matter of homosexual sex.

"Homosexual sex is bad because it spreads stds."

It is not objectively true that it is immoral, this is subjective opinion. The statement contains an inaccurate but partial truth, then makes a subjective claim it is bad, it's the second part you would need to demonstrate is objectively true, without resorting to a subjective opinion. 
If we agree with the subjective claim that result X is immoral,  then we can make an objectively true claim that actions that cause X are immoral, but ultimately they still rest on a subjective opinion. 

2. Homosexual sex is bad because it erodes the traditional family.
2. I am dubious this is true, as it seems like a slippery slope fallacy to me. 

It's objectively true but not an objectivist objection.   It is the claim that homosexual sex is bad because of some fact about our relativist norms, rather than homosexual sex.

Again even were it true that behaviour X erodes the traditional family, I don't see it is objectively true that eroding the traditional family is immoral, rather this is a subjective claim, as will be the claims that support why anyone thinks this I suspect. 

Another objectively true statement but not an objectivist objection.  It is the claim that homosexual sex is bad because some subject..god in this case, is against it.

It is only objectively true if you can objectively demonstrate a deity exists and thinks this, but even then, the assertion it is immoral would be a subjective one, even from a deity, why would it be otherwise?

4. By this rationale garden peas would be immoral for me. 

Correct...or, that immoral was garden peas. Where's the clownface emoji?

That a person finds behaviour X immoral because it is repulsive, might be true, but it does not follow that behaviour X is objectively immoral. 

So if for example, we agreed that causing unnecessary harm was immoral, we could then of course make objective claims, for example: kicking someone without any reason causes harm, ipso facto it is immoral, but it rests on a subjective moral assertion. If one asks why something is immoral, it ultimately rests on a subjective assertion.