No. Governments start wars. Governments keep wars going. Those Governments have historically been made up by a very particular class of people and yes, usually men. That means we can either see this as a class issue or a sex issue. Given that wars keep happening but we have people like Margaret Thatcher and Hilary Clinton failing to stop them (and in some cases helping to continue them) - I think what we have here is an issue based in class rather than sex.
I don't expect anyone to prioritise male conscription, in fact I think the ideal position is zero conscription. If you are going to have conscription then it needs to be fairly distributed across a population according to requirement, not a prima-facie judgment on sex alone. Because making a judgment on sex alone is.... sexism.
When you say 'we have our own problems' you suggest that what you really mean is that you aren't interested in the underlying equality based in human rights, you're interested in those arguments that align with your genitals and that can be used solely for your agenda. There are plenty of men who can and do stand with you on basic human rights in the same way there are plenty of women who don't - but this isn't even that. This is simply an understanding of the principle of equality underlying feminism and seeing where fourth wave feminism occasionally misses the mark.