First of all, not being proud of something is not the same as being ashamed of it. There is a spectrum. You can just be something without it being a point of pride. Pride should be something that is earned as one accomplished something or overcomes some struggle. It should not be the default. It's dumb to be proud to be a Gemini, proud to be 23 years old, or proud to be named "David". You have nothing to do with being those things and none of those things inherently cause you struggles. Can you think of any similar attributes that are stupid to be proud of?
Second of all, many minorities are proud not simply because they are a minority, but because they've had to deal with the challenges that are the default state of being part of that minority in our society. As an example, "gay pride" is about being open, honest and okay with who you are despite a very recent history where being outed as gay meant you were a punchline, at best, and hated, violated and killed, at worst. It is about overcoming obstacles. Struggles. The same applies to other marginalized minorities, racial minorities, religious minorities, immigrants, trans people, etc. It is not about feeling self-righteous, superior, or owed more than anyone else. It is about climbing from the pit that society put you in and fighting your way to stand level with everyone else.
That is why straight pride and white pride are usually synonymous with ignorant or hateful people. When you are not only in the majority, but also part of the group that is ultimately responsible for marginalizing minorities, whether you specifically do it or not, the context of your pride in those attributes is inherently different. Reflecting back "gay pride" with "straight pride" or "black pride" with "white pride" is not just about being ok with your orientation or race. It IS ok to be straight and white, as well as American, Christian, cis, male, etc.. But those attributes do not, in themselves, cause you struggle. You're not marginalized because of those attributes. You are not celebrating what you have overcome. You are rebutting someone who is proud of being gay, black, etc. and their accomplishments in overcoming their struggles with "Well if you can be proud about that, I can be proud about being not that, too!". You're at best missing the point and childishly making something about you that is NOT about you. And, at worst, you're suggesting that you shouldn't be proud to be gay, black, trans, foreign, non-christian, etc. at all. Either way, it's not innocent or the "same thing".
Sincerely, a straight white cis American-by-birth man who is not ashamed or proud of any of those attributes.