For me it was a long way...
I was quite young when started feeling this curiosity and desire to experience it, and didn't feel bad about it. Then, after my first experience i felt ashamed, too guilty, felt like i was a trash person who didn't deserve anything good in life. For many years after that i tried to be a "normal" guy, to forget that and avoid everything related. In that time i change my mind a bit. Grown up and realized than i worried a lot about what was correct for society or what people thought.
There's social stigma towards things that aren't that bad at all, and that stigma change over time and region, so i don't care too much about it right now. Now i use my own judgement and see this just as something, not bad nor good, just something.
Also worth mentioning that internet allowed me to found other people that had struggle with similar situations. The few people i've in contact with (hope will be more in the future) are just normal people who just happens likes animals in this way. No horrible trash person who deserves everything bad, or monsters without feelings, just people.
To this day i don't think i've accepted myself 100%, but close. Feel way more comfortable with the fact that i like this. I even had a recent experience that i enjoyed a lot and feel ok with that, without all the awful feelings from the first experience.