Many states in the US are confirming there is community spread happening, i.e. it's not restricted to a subset of the gay or hetero community. Here's Seattle for example confirming there are cases with no known sexual encounter or link: https://publichealthinsider.com/2022/07/06/monkeypox-update-...
Yes, there are non-gay people who get it. But gay men, and particularly people who have sex with a dozen different partners in a week (not many straight men in that particular group), are much more likely to contract it. Efforts to limit the spread of monkeypox should be targeted at the demographics most likely to contract it, as you get much more bang-for-buck that way.
There is nothing inherent about the DNA of this virus that makes it target men, gay men, or men who have sex with men. It will infect any human in the wrong place at the wrong time, period.
Given that monkeypox disproportionately affects gay men, your proposed policy would require the government to somehow identify that population, engage in regular mass testing of them and then actively police them to prevent them going out and infecting other people. Remember that tests have false positives. Many of the people who tested positive for COVID had no symptoms at all, or symptoms so mild they'd hardly noticed, so you can bet that mass testing for monkeypox would yield some steady stream of FPs as well.
You really think that's going to happen? If you think our governments would even countenance that policy for a second when it'd disproportionately impact LGBT people then, well, you don't live on the same planet as I do!
Congrats for making quite possibly the greatest leap since Armstrong stepped off Apollo 11.