The number of applications to change the gender in one's passport will grow with each incident or legislation that makes the draft more likely since the constitution states that only citizens designated 'male' in their passports are to be drafted. Is there a downside to changing it to 'divers' or 'keine Angabe' (not specified)?

Here's the main reason I think most people are going to try to avoid a draft. Politicians have destroyed Germany and its future while they enriched themselves and their rich friends, for example [1]. They have lured in a flood of migrants against the will of many natives. They have been transferring wealth of the natives to the migrants by printing money to give to the migrants, thereby generating inflation while overloading all kinds of services. Even medium-sized cities in the east of Germany are infested with unwanted, culturally incompatible, sketchy male immigrants loitering around in groups, making people feel unsafe in their own cities. These people are disproportionately more responsible for violent crime, such as knife attacks or gang rape. You could halve gang rape by throwing out certain migrant groups. Yet nothing effective has been done by the government. Recently, there was a case in a youth club in the notoriously high-immigrant Berlin district Neukölln, where a 16-year-old girl said she was raped by a Muslim male. She said this was video recorded and used by a group of boys to extort her. The Jugendamt (child protective services) was informed, which is reported to have refused to file a charge with the police "because it marginalizes the perpetrator group" and "the Muslim boys are already under enough police scrutiny".

Who wants to fight for that? There is little patriotism. The rich live lavishly off their Rheinmetall stocks, many refugees live very well from welfare and child benefits, and the immigrant criminals live off their ill-gotten gains without effective prosecution or punishment. None of those will be drafted; only the ordinary German will. Many of them are furious; the others are misinformed or uninformed. If the politicians try to draft the really angry people, the angry people might decide to pay them a visit instead.

[1] (in German) https://correctiv.org/thema/aktuelles/das-spahn-netzwerk/